1,1

No other terms < 6500000 - John Blazek, May 14 2009

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 115, p. 40, Ellipses, Paris 2008.

H. Riesel, Lucasian criteria for the primality of N=h.2^n-1, Math. Comp., 23 (1969), 869-875.

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

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

Ray Ballinger, Woodall Primes: Definition and Status

Ray Ballinger and Wilfrid Keller, Woodall numbers

C. K. Caldwell, Woodall Numbers

J. DeMaio, Generalized Woodall Numbers

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

Eric Weisstein's World of Mathematics, Woodall Numbers

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Cf. A050918 (for the actual primes), A003261, A005849.

Sequence in context: A018318 A051717 A108326 this_sequence A074005 A145499 A082611

Adjacent sequences: A002231 A002232 A002233 this_sequence A002235 A002236 A002237

nonn,nice,hard

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

a(27) communicated by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 15 2004

1195203 found by M. Rodenkirch, but the region from 1020000 to 1195203 is incompletely searched; contributed by Eric Weisstein (eric(AT)weisstein.com), Nov 29, 2005

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

1467763, 2013992, 2367906, 3752948 from John Blazek, May 14 2009

1,1

p and q cannot both be odd. Thus p=2 or q=2. If q=2 then we want primes of form p^2+8. But 8=-1 mod 3. Since p is prime, p=3 or == 1 or 2 mod 3. If p=1 or 2 mod 3 then 3|p^2+8, so p=3. Therefore with the exception of the first entry (3^2+8=17) this sequence is really just primes of the form q^3+4.

For example: 6863=19^3+2^2.

for n from 1 to 1000 do if (isprime((ithprime(n))^3+4)) then print((ithprime(n))^3+4, 4); fi; if (isprime((ithprime(n))^2+8)) then print((ithprime(n))^2+8, 8); fi; od;

Cf. A045699.

Sequence in context: A163443 A027722 A060342 this_sequence A146800 A146731 A146667

Adjacent sequences: A045697 A045698 A045699 this_sequence A045701 A045702 A045703

nice,nonn,easy

Felice Russo (felice.russo(AT)katamail.com)

Extension and comment from Joe DeMaio (jdemaio(AT)kennesaw.edu)

1,1

Starting with 3rd term, 22501, all terms are of the form 900n^2+1 with n=5, 6, 8, 9, 14, 19, 43, 44, 77, 85 (A125251) [From Zak Seidov (zakseidov(AT)yahoo.com), Dec 07 2008]

{A037074(k) + 2} INTERSECT {A000040}. {A001359(k) * A006512(k) + 2} INTERSECT {A000040}. {A054735(k)^2 + 2*A054735(k) + 2} INTERSECT {A000040}. - Jonathan Vos Post (jvospost3(AT)gmail.com), May 11 2006

The third term 22501 is a member of the sequence because 22501=149*151+2, 22501 is prime and {149,151} is a twin prime pair.

with (numtheory): for n from 1 to 2000 do if (ithprime(n+1)-ithprime(n)=2) then if (tau(ithprime(n)*ithprime(n+1)+2)=2) then print(ithprime(n), ithprime(n+1), ithprime(n)*ithprime(n+1)+2); fi; fi; od;

lst={}; Do[p=Prime[n]; If[Length[Divisors[p-2]]==4&&(Divisors[p-2][[3]]-Divisors[p-2][[2]])==2, AppendTo[lst, p]], {n, 6*10^5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 08 2008]

Cf. A048880, A051779, A000040, A001359, A005384, A006512, A037074, A054735.

A125251 [From Zak Seidov (zakseidov(AT)yahoo.com), Dec 07 2008]

Sequence in context: A093343 A153685 A121710 this_sequence A139579 A125248 A156777

Adjacent sequences: A051776 A051777 A051778 this_sequence A051780 A051781 A051782

easy,nonn

Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 09 1999

Edited by R. J. Mathar, Aug 08 2008

1,1

T. D. Noe, Table of n, a(n) for n=1..1000

487*491+2=239119.

with (numtheory): for n from 1 to 1000 do if (tau(ithprime(n)*ithprime(n+1)+2)=2) then print(ithprime(n), ithprime(n+1), ithprime(n)*ithprime(n+1)+2); fi; od;

ct = 0; Do[If[PrimeQ[Prime[k]*Prime[k + 1] + 2], ct++; n[ct] = Prime[k]*Prime[k + 1] + 2], {k, 1, 430}]; Table[n[k], {k, 1, ct}] (Lei Zhou)

Cf. A051507.

Sequence in context: A146348 A050952 A093930 this_sequence A075892 A155143 A141886

Adjacent sequences: A048877 A048878 A048879 this_sequence A048881 A048882 A048883

easy,nonn,nice

Herman H. Rosenfeld (herm3(AT)pacbell.net)

Corrected and extended by Joe DeMaio (jdemaio(AT)kennesaw.edu).

0,1

Sequence is ordered by size of n not size of C(n,k). Link gives list of all values up to n=1352.

More terms

C(11,5)=462 is a member of the sequence because 461 and 463 are twin primes.

See A051770 for values of n, A051771 for values of k.

Sequence in context: A000410 A028665 A001328 this_sequence A024084 A132590 A112945

Adjacent sequences: A051732 A051733 A051734 this_sequence A051736 A051737 A051738

nonn

Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 06 1999

1,1

The integer 202 occurs twice because both C(202,34) and C(202,69) yield twin prime pairs.

Source

The integer 11 is a member of the sequence because C(11,5)=462 and 461 and 463 are twin primes.

A051735, A051771.

Sequence in context: A149316 A149317 A027042 this_sequence A032181 A081073 A002831

Adjacent sequences: A051767 A051768 A051769 this_sequence A051771 A051772 A051773

nonn

Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 08 1999

0,1

This sequence is ordered by the size of the corresponding value of n.

Source

The integer 5 is a member of the sequence because C(11,5)=462 and 461 and 463 are twin primes.

A051735, A051770.

Sequence in context: A139007 A015486 A120767 this_sequence A008318 A160048 A019047

Adjacent sequences: A051768 A051769 A051770 this_sequence A051772 A051773 A051774

nonn

Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 08 1999

1,1

F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 1993.

M. L. Perez et al., eds., Smarandache Notions Journal

F. Smarandache, Only Problems, Not Solutions!

Sequence in context: A091898 A061365 A102107 this_sequence A076055 A068653 A102616

Adjacent sequences: A007932 A007933 A007934 this_sequence A007936 A007937 A007938

nonn,base,easy

R. Muller

More terms from Joe DeMaio (jdemaio(AT)kennesaw.edu)

1,1

Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers, Prometheus Books, NY, 2007, page 93.

C(10,5)=252. 3003 occurs thrice because C(14,6)=C(15,5)=C(78,2)=3003.

fQ[n_] := Block[{id = IntegerDigits@n}, id == Reverse@id]; lst = {}; Do[ k = 2; While[k < n/2 + 1, b = Binomial[n, k]; If[fQ@b, AppendTo[lst, b]; Print@b]; k++ ], {n, 25000000}]; Take[ Union@ lst, 35] - Robert G. Wilson v

Cf. A002113, A006987.

Sequence in context: A132474 A032070 A066569 this_sequence A003098 A045914 A067610

Adjacent sequences: A051638 A051639 A051640 this_sequence A051642 A051643 A051644

nonn,base,nice,easy

Joe DeMaio (jdemaio(AT)kennesaw.edu)

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 20 2000

1,1

Values have been checked up to n=100000.

S(16,4)=171798901 and S(40,4)=50369882873307917364901 are both prime numbers.

Do[ If[ PrimeQ[ StirlingS2[n, 4]], Print[n]], {n, 4, 11000, 4}] (from Robert G. Wilson v Jan 14 2005)

Sequence in context: A070584 A132161 A086046 this_sequence A044093 A044474 A134593

Adjacent sequences: A100955 A100956 A100957 this_sequence A100959 A100960 A100961

nonn

Joe DeMaio, Stephen Touset (jdemaio(AT)kennesaw.edu), Jan 11 2005