|
%I #34 Feb 16 2021 00:58:40
%S 3,5,7,13,19,31,43,61,73,103,109,139,151,181,193,199,229,241,271,283,
%T 313,349,421,433,463,523,571,601,619,643,661,811,823,829,859,883,1021,
%U 1033,1051,1063,1093,1153,1231,1279,1291,1303,1321,1429,1453,1483,1489
%N Primes p such that sigma(p-2) < p.
%C Also, apart from the first term, greater members of twin prime pairs: A006512(n) = a(n+1). - _Reinhard Zumkeller_, Dec 07 2002
%C Smallest prime > n-th odd number that is the difference of 2 primes. - _Juri-Stepan Gerasimov_, Nov 08 2010
%C 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
%t Select[Prime@ Range@ 240, DivisorSigma[1, # - 2] < # &] (* _Michael De Vlieger_, Jun 12 2015 *)
%o (PARI) lista(nn) = forprime(p=3, nn, if (sigma(p-2) < p, print1(p, ", "));); \\ _Michel Marcus_, Jun 06 2015
%Y Cf. A025584, A001359, A006512, A000203.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Feb 08 2002
|
