cp's OEIS Frontend

A281317 Primes p such that p == i mod d(i) where d(i) are the prime divisors of 2p+1.

%I A281317 #8 Jan 20 2017 13:44:39
%S A281317 7,13,37,67,157,337,367,607,787,937,1093,3037,3307,7717,9187,12757,
%T A281317 15187,19687,27337,35437,42187,49207,69457,75937,267907,347287,683437,
%U A281317 744187,797161,882367,1148437,1458607,1736437,2067187,2870437,2929687,3125587,4823437
%N A281317 Primes p such that p == i mod d(i) where d(i) are the prime divisors of 2p+1.
%C A281317 Subsequence of A053176.
%C A281317 a(n)== 1 mod 6 or a(n)== 1, 7 mod 12. A majority of members of the sequence are congruent to 7 mod 10.
%C A281317 omega(2*a(n)+1) = 1 for n = 2, 11, 29,... => 2*a(n)+1 = 3^3, 3^7, 3^13,... where omega(n) = A001221(n).
%e A281317 157 is in the sequence because  2*157 + 1 = 315 = 3 ^ 2 * 5 * 7 => 157 == 1 (mod 3), 157 == 2 (mod 5) and 157 == 3 (mod 7).
%p A281317 with(numtheory):
%p A281317 for n from 2 to 10^5 do:
%p A281317   p:=ithprime(n):q:=2*p+1:x:=factorset(q):n1:=nops(x):j:=0:
%p A281317    for i from 1 to n1 do:
%p A281317      if irem(p,x[i])=i
%p A281317       then j:=j+1:
%p A281317       else
%p A281317      fi:
%p A281317    od:
%p A281317     if j=n1
%p A281317      then
%p A281317      printf(`%d, `,p):
%p A281317      else
%p A281317     fi:
%p A281317   od:
%t A281317 Select[Prime@ Range[10^6], Function[p, Function[i, Times @@ Boole@ MapIndexed[Mod[p, #1] == First@ #2 &, FactorInteger[i][[All, 1]]] > 0][2 p + 1]]] (* _Michael De Vlieger_, Jan 20 2017 *)
%Y A281317 Cf. A001221, A053176, A053177.
%K A281317 nonn
%O A281317 1,1
%A A281317 _Michel Lagneau_, Jan 20 2017