|
| |
|
|
A002476
|
|
Primes of form 6n + 1.
(Formerly M4344 N1819)
|
|
96
| |
|
|
7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613, 619
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Equivalently, primes of the form 3n + 1.
Primes p dividing sum(k=0,p,C(2k,k)) -3 = A006134(p)-3 - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 08 2003
Primes p such that tau(p)==2 (mod 3) where tau(x) is the Ramanujan tau function (cf. A000594). - Benoit Cloitre (benoit7848c(AT)orange.fr), May 04 2003
Primes of the form x^2-xy+7y^2 with x and y nonnegative. - T. D. Noe (noe(AT)sspectra.com), May 07 2005
Primes p such that p^2 divides Sum[Sum[(2k)!/(k!)^2,{k,1,m}],{m,1,2(p-1)}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006
A039701(A049084(a(n))) = A134323(A049084(a(n))) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 21 2007
The set of primes of the form 3n + 1 is a superset of the set of greater of twin primes larger than five (A006512). - Paul Muljadi (paulmuljadi(AT)yahoo.com), Jun 05 2008
Also primes p such that the arithmetic mean of divisors of p^2 is an integer : sigma_1(p^2)/sigma_0(p^2) = C. (A000203(p^2)/A000005(p^2) = C) [From Ctibor O. Zizka (c.zizka(AT)email.cz), Sep 15 2008]
Is this the same sequence as A139492?
|
|
|
REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
K. G. Reuschle, Tafeln Complexer Primzahlen. K\"{o}nigl. Akademie der Wissenschaften, Berlin, 1875, p. 1.
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).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
C. Banderier, Calcul de (-3/p)
A. Granville and G. Martin, Prime number races
|
|
|
FORMULA
| Sum_{n>=1} 1/a(n)^2 = A175644. Sum_{n>=1} 1/a(n)^3 = A175645. - R. J. Mathar, Apr 03 2011
|
|
|
MAPLE
| a := [ ]: for n from 1 to 400 do if isprime(6*n+1) then a := [ op(a), n ]; fi; od: A002476 := n->a[n];
|
|
|
MATHEMATICA
| Select[6*Range[100] + 1, PrimeQ[ # ] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 06 2006
|
|
|
PROG
| (MAGMA) [n: n in [1..700 by 6] | IsPrime(n)]; // Vincenzo Librandi, Apr 05 2011
|
|
|
CROSSREFS
| Cf. A045331.
For values of n see A024899. Primes of form 3n-1 give A003627.
These are the primes arising in A024892, A024899, A034936, A091178 gives prime index.
Cf. A006512.
Sequence in context: A107925 * A123365 A144921 A040079 A038160 A106870
Adjacent sequences: A002473 A002474 A002475 * A002477 A002478 A002479
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
