30,2

See Table 4 column 6 of Brinkmann et al. paper.

G. Brinkmann, G. Caporossi and P. Hansen, "A survey and new results on computer enumeration of polyhex and fusene hydrocarbons", J. Chem. Inf. Comput. Sci., vol. 43 (2003), pp. 842-851.

If n=30 then the number of benzenoids with 21 hexagons with C_(2h) symmetry is 1 which is the first term in the sequence.

Sequence in context: A098385 A048364 A141549 this_sequence A147208 A010003 A007587

Adjacent sequences: A121961 A121962 A121963 this_sequence A121965 A121966 A121967

nonn

Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Sep 10 2006

1,1

C. K. Caldwell and Y. Gallot, On the primality of n!+-1 and 2*3*5*...*p+-1, Math. Comp., 71 (2001), 441-448.

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 211, p. 61, Ellipses, Paris 2008.

H. Dubner, A new primorial prime, J. Rec. Math., 21 (No. 4, 1989), 276.

R. K. Guy, Unsolved Problems in Number Theory, Section A2.

Paulo Ribenboim, The New Book of Prime Number Records, p. 13.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

C. K. Caldwell, Primorial Primes

R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

A014545 gives same sequence in another form, namely values of n such that 1 + product of first n primes is prime. Cf. A002110, A006862, A006794, A057704. A018239 gives the actual primes.

Sequence in context: A119388 A093487 A067933 this_sequence A141500 A059999 A040130

Adjacent sequences: A005231 A005232 A005233 this_sequence A005235 A005236 A005237

nonn,hard,nice

N. J. A. Sloane (njas(AT)research.att.com).

42209 sent in by Chris Nash (chrisnash(AT)cwix.com).

145823 discovered and sent in by Arlin Anderson (starship1(AT)gmail.com) and Don Robinson (donald.robinson(AT)itt.com), Jun 01 2000

366439, 392113 from Eric Weisstein (eric(AT)weisstein.com), Mar 13 2004 (based on information in A057704)

13,1

The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(7)=1086400325525346, a(10)=2677889, a(11)=757074, a(8) and a(9) seem not to exist.

M. R. Diamond and D. D. Reidpath, A counterexample to a conjuncture of Sloane and Erdos, J. Recreational Math., 1998 29(2), 89-92. [Broken link?]

Sascha Kurz, Persistence in different bases

C. Rivera, Minimal prime with persistence p

N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.

Eric Weisstein's World of Mathematics, Multiplicative Persistence

a(n) = 9*n-[n/40320] for n > 40319

a(13)=7577 because 7577 is the fewest number with persistence 8 in base 13.

Cf. A003001, A031346, A064867, A064868, A064869, A064870, A064871.

Sequence in context: A031675 A031585 A031765 this_sequence A028539 A031854 A068245

Adjacent sequences: A064869 A064870 A064871 this_sequence A064873 A064874 A064875

base,easy,nonn

Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Oct 08 2001

1,1

fQ[n_]:=PrimeQ[n^2-42]&&PrimeQ[n^2+42]; lst={}; Do[If[fQ@Prime[n], AppendTo[lst, Prime[n]]], {n, 7!}]; lst

Cf. A153116, A153119

Sequence in context: A140565 A079732 A161540 this_sequence A115782 A051654 A098973

Adjacent sequences: A153117 A153118 A153119 this_sequence A153121 A153122 A153123

nonn

Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 18 2008

1,1

Subsequence of A005385.

For p = 2 (the only case with p+1 odd), 2*p+1 = 5 is prime and p+1 = 3 is square-free, so 5 is in the sequence. For p = 3, 2*p+1 = 7 is prime and p+1 = 4 is not square-free, so 7 is not in the sequence.

<< NumberTheory`NumberTheoryFunctions` lst={}; Do[p=Prime[n]; If[PrimeQ[Floor[p/2]]&&SquareFreeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst

(MAGMA) [ q: p in PrimesUpTo(8100) | IsSquarefree(p+1) and IsPrime(q) where q is 2*p+1 ];

Cf. A005117 (square-free numbers), A005385 (safe primes p: (p-1)/2 is also prime), A153207, A153208, A153210.

Sequence in context: A070198 A121934 A153812 this_sequence A106257 A104358 A104359

Adjacent sequences: A153206 A153207 A153208 this_sequence A153210 A153211 A153212

nonn

Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 20 2008

Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 24 2008

1,2

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Jackson, D. M.; Reilly, J. W. Permutations with a prescribed number of p-runs. Ars Combinatoria 1 (1976), number 1, 297-305.

J. Riordan, Permutations without 3-sequences, Bull. Amer. Math. Soc., 51 (1945), 745-748.

Jackson, D. M. and Read, R. C., A note on permutations without runs of given length, Aequationes Math. 17 (1978), number 2-3, 336-343.

seq(coeff(convert(series(add(m!*((t-t^3)/(1-t^3))^m, m=0..50), t, 50), polynom), t, n), n=1..25); (Pab Ter)

Cf. A047921.

Cf. A165960, A165961, A165962. [From Isaac E. Lambert (lamberti09(AT)mail.wlu.edu), Oct 07 2009]

Sequence in context: A008981 A008982 A130471 this_sequence A020129 A129582 A152576

Adjacent sequences: A002625 A002626 A002627 this_sequence A002629 A002630 A002631

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005

1,1

Eric Weisstein, Link to a section of The World of Mathematics. Harmonic Number.

A027612(n) begins {1, 5, 13, 77, 87, 223, 481, 4609, 4861, ...}.

Thus a(1) = 2, a(2) = 3, a(3) = 6, a(4) = 9.

s=1; Do[s=s+1/(n+1); f=Numerator[(n+1)*(s-1)]; If[PrimeQ[f], Print[{n, f}]], {n, 1, 1942}]

A027612(n) are the numerators of second order harmonic numbers H(n, (2)) = Sum[HarmonicNumber[k], {k, 1, n}]. Corresponding primes in A027612(n) are listed in A124878(n) = A027612[ a(n) ] = {5, 13, 223, 4861, 197698279, 25472027467, 6975593267347, 218572480850557, 1592457339642613, ...}.

Cf. A001008, A002805, A067657, A056903, A027612, A124878, A124837, A124880, A124881.

Sequence in context: A018251 A018402 A018441 this_sequence A062865 A018264 A081741

Adjacent sequences: A124876 A124877 A124878 this_sequence A124880 A124881 A124882

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 11 2006

More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 29 2007

0,2

J. Riordan, Permutations without 3-sequences, Bull. Amer. Math. Soc., 51 (1945), 745-748.

Reference gives a recurrence.

1; 2; 5 1; 21 2 1; 106 11 2 1; ...

Columns give A002628, A002629, A002630.

Sequence in context: A106852 A162975 A120294 this_sequence A102786 A159985 A146103

Adjacent sequences: A047918 A047919 A047920 this_sequence A047922 A047923 A047924

nonn,tabl,nice,easy,more

N. J. A. Sloane (njas(AT)research.att.com).

0,1

E.g. 5*7=17+19-1,11*13=71+73-1.

Cf. A047977-A047979.

Sequence in context: A046121 A023271 A159049 this_sequence A006382 A055113 A129015

Adjacent sequences: A047973 A047974 A047975 this_sequence A047977 A047978 A047979

nonn

Naohiro Nomoto (6284968128(AT)geocities.co.jp)

1,1

Gilberto Garcia-Pulgarin, Numeros de Carmichael producto de tes primos, preprint, 1999.

Index entries for sequences related to Carmichael numbers.

2 is in the sequence since is no Carmichael number of the form 2rq.

Sequence in context: A132871 A140314 A092730 this_sequence A070256 A020450 A036229

Adjacent sequences: A051660 A051661 A051662 this_sequence A051664 A051665 A051666

nonn

Gilberto Garcia-Pulgarin (gigarcia(AT)e-math.ams.org)

Edited by Jack Brennen, Jul 01 2008