A067829 Primes p such that sigma(p-2) < p.

3, 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489

Offset: 1

Author

Benoit Cloitre, Feb 08 2002

Keywords

• nonn

Comments

Also, apart from the first term, greater members of twin prime pairs: A006512(n) = a(n+1). - Reinhard Zumkeller, Dec 07 2002

Smallest prime > n-th odd number that is the difference of 2 primes. - Juri-Stepan Gerasimov, Nov 08 2010

These primes are the only primes, p(j) = A000040(j), such that (p(j)-p(j-m)) divides (p(j)+p(j-m)) for some m, 0 < m < j. For all such cases, m=1. It is easy to prove for j-m>1 the only common factor of (p(j)-p(j-m)) and (p(j)+p(j-m)) is 2, and there are no common factors if j-m = 1. Thus, p(j-m) is the lesser member of a twin prime pair, except when j=2. - Richard R. Forberg, Mar 25 2015

Links

• Robert Price, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025584, A001359, A006512, A000203.

Programs

Mathematica

Select[Prime@ Range@ 240, DivisorSigma[1, # - 2] < # &] (* Michael De Vlieger, Jun 12 2015 *)

PARI

lista(nn) = forprime(p=3, nn, if (sigma(p-2) < p, print1(p, ", "));); \\ Michel Marcus, Jun 06 2015