|
Search: 2, 5, 11, 31
|
|
|
| A124481 |
|
Number of connected hook length posets, with n elements. |
|
+20
5
|
| |
|
|
|
|
|
|
| A139464 |
|
Numbers of the form n!+2n-1. |
|
+20
4
|
|
| 2, 5, 11, 31, 129, 731, 5053, 40335, 362897, 3628819, 39916821, 479001623, 6227020825, 87178291227, 1307674368029, 20922789888031, 355687428096033, 6402373705728035, 121645100408832037, 2432902008176640039
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
F. Luca and I. E. Shparlinsky, 2005. On the largest prime factor of n! + 2n - 1. J. Th. des Nombres de Bordeaux Vol.17, Fasc. 3
|
|
MATHEMATICA
|
Table[n! + 2 n - 1, {n, 1, 40}]
|
|
CROSSREFS
|
Cf. A127986, A127987, A139023, A139024, A139465, A139466, A139467.
Sequence in context: A139467 A124481 A002862 this_sequence A101837 A124483 A079571
Adjacent sequences: A139461 A139462 A139463 this_sequence A139465 A139466 A139467
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Artur Jasinski (grafix(AT)csl.pl), Apr 22 2008
|
|
|
|
|
| A139466 |
|
Smallest prime factor of n! + 2n - 1. |
|
+20
4
|
|
| 2, 5, 11, 31, 3, 17, 31, 3, 362897, 3628819, 3, 251, 5, 3, 93407, 200989, 3, 5, 211, 3, 199, 38189, 3, 314707, 7, 3, 2473, 5, 3, 98274048659069, 1447, 3, 5, 585341, 3, 61, 8150209692797, 3, 7, 131
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
F. Luca and I. E. Shparlinsky, 2005. On the largest prime factor of n! + 2n - 1. J. Th. des Nombres de Bordeaux Vol.17, Fasc. 3
|
|
MATHEMATICA
|
a = {}; Do[AppendTo[a, n! + 2 n - 1], {n, 1, 40}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = c[[1]]; AppendTo[b, d[[1]]], {n, 1, Length[a]}]; b (*Artur Jasinski*)
|
|
CROSSREFS
|
Cf. A127986, A127987, A139023, A139024, A139464, A139465, A139467.
Sequence in context: A144959 A131347 A079225 this_sequence A139467 A124481 A002862
Adjacent sequences: A139463 A139464 A139465 this_sequence A139467 A139468 A139469
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Artur Jasinski (grafix(AT)csl.pl), Apr 22 2008
|
|
|
|
|
| A139467 |
|
Largest prime factor of n! + 2n - 1. |
|
+20
4
|
|
| 2, 5, 11, 31, 43, 43, 163, 2689, 362897, 3628819, 179, 1908373, 800903, 101341, 13999747, 104099179, 10778406912001, 1300448327, 356961701, 62382102773760001, 10367823077693, 11437176299, 102338720137
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
F. Luca and I. E. Shparlinsky, 2005. On the largest prime factor of n! + 2n - 1. J. Th. des Nombres de Bordeaux Vol.17, Fasc. 3
|
|
MATHEMATICA
|
a = {}; Do[k = n! + 2 n - 1; c = First[Last[FactorInteger[k]]]; AppendTo[a, c], {n, 1, 40}]; a (*Artur Jasinski*)
|
|
CROSSREFS
|
Cf. A127986, A127987, A139023, A139024, A139464, A139465, A139466.
Sequence in context: A131347 A079225 A139466 this_sequence A124481 A002862 A139464
Adjacent sequences: A139464 A139465 A139466 this_sequence A139468 A139469 A139470
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Artur Jasinski (grafix(AT)csl.pl), Apr 22 2008
|
|
|
|
|
| A002862 |
|
Number of nonisomorphic connected functions with no fixed points, or proper rings with n edges.
(Formerly M1403 N0547)
|
|
+20
3
|
|
| 0, 1, 2, 5, 11, 31, 77, 214, 576, 1592, 4375, 12183, 33864, 94741, 265461, 746372, 2102692, 5938630, 16803610, 47639902, 135288198, 384812502, 1096141974, 3126648842, 8929715592, 25533447030
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
REFERENCES
|
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).
R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 41.399.
|
|
CROSSREFS
|
(A002861) minus (A000081).
Sequence in context: A139466 A139467 A124481 this_sequence A139464 A101837 A124483
Adjacent sequences: A002859 A002860 A002861 this_sequence A002863 A002864 A002865
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from and better description from Christian Bower (bowerc(AT)usa.net)
|
|
|
|
|
| A060441 |
|
Triangle T(n,k), n >= 0, in which n-th row (for n >= 3) lists prime factors of Fibonacci(n) (see A000045), with repetition. |
|
+20
3
|
|
| 0, 1, 1, 2, 3, 5, 2, 2, 2, 13, 3, 7, 2, 17, 5, 11, 89, 2, 2, 2, 2, 3, 3, 233, 13, 29, 2, 5, 61, 3, 7, 47, 1597, 2, 2, 2, 17, 19, 37, 113, 3, 5, 11, 41, 2, 13, 421, 89, 199, 28657, 2, 2, 2, 2, 2, 3, 3, 7, 23, 5, 5, 3001, 233, 521, 2, 17, 53, 109, 3, 13, 29, 281, 514229, 2, 2, 2, 5, 11, 31, 61
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Rows have irregular lengths.
|
|
EXAMPLE
|
0; 1; 1; 2; 3; 5; 2,2,2; 13; 3,7; 2,17; ...
|
|
MAPLE
|
with(combinat); A060441 := n->ifactor(fibonacci(n));
with(numtheory): with(combinat): for i from 3 to 50 do for j from 1 to nops(ifactors(fibonacci(i))[2]) do for k from 1 to ifactors(fibonacci(i))[2][j][2] do printf(`%d, `, ifactors(fibonacci(i))[2][j][1]) od: od: od:
|
|
CROSSREFS
|
A000045, A060442.
Sequence in context: A094122 A082117 A011157 this_sequence A065996 A133906 A133907
Adjacent sequences: A060438 A060439 A060440 this_sequence A060442 A060443 A060444
|
|
KEYWORD
|
nonn,tabf,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Apr 07 2001
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 09 2001
|
|
|
|
|
| A060442 |
|
Triangle T(n,k), n >= 0, in which n-th row (for n >= 3) lists prime factors of Fibonacci(n) (see A000045), without repetition. |
|
+20
3
|
|
| 0, 1, 1, 2, 3, 5, 2, 13, 3, 7, 2, 17, 5, 11, 89, 2, 3, 233, 13, 29, 2, 5, 61, 3, 7, 47, 1597, 2, 17, 19, 37, 113, 3, 5, 11, 41, 2, 13, 421, 89, 199, 28657, 2, 3, 7, 23, 5, 3001, 233, 521, 2, 17, 53, 109, 3, 13, 29, 281, 514229, 2, 5, 11, 31, 61, 557, 2417, 3, 7, 47, 2207, 2, 89
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Rows have irregular lengths.
|
|
LINKS
|
T. D. Noe, Rows n=0..1000 of triangle, flattened (using Blair Kelly's data)
Blair Kelly, Fibonacci and Lucas Factorizations
|
|
EXAMPLE
|
0; 1; 1; 2; 3; 5; 2; 13; 3,7; 2,17; ...
|
|
MAPLE
|
with(numtheory): with(combinat): for i from 3 to 50 do for j from 1 to nops(ifactors(fibonacci(i))[2]) do printf(`%d, `, ifactors(fibonacci(i))[2][j][1]) od: od:
|
|
CROSSREFS
|
A000045, A060441.
For n>2, the length of row n is A022307(n).
Sequence in context: A102867 A139044 A060383 this_sequence A060385 A080648 A113195
Adjacent sequences: A060439 A060440 A060441 this_sequence A060443 A060444 A060445
|
|
KEYWORD
|
nonn,tabf,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Apr 07 2001
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 09 2001
|
|
|
Search completed in 0.007 seconds
|
