A181938 - OEIS

%I #14 Aug 03 2014 14:01:26

%S 7,13,19,43,97,103,109,127,139,181,193,229,241,283,307,313,349,397,

%T 409,421,457,463,487,499,643,691,709,769,787,811,823,829,853,859,877,

%U 883,907,919,937,967,1021,1051,1093,1153,1171,1279,1303,1423,1429,1447,1483

%N Isolated primes = 1 mod 6: sandwiched by primes = 5 mod 6.

%C Primes p(m) = 1 mod 6 such that both p(m-1) and p(m+1) are congruent to 5 mod 6.

%C Corresponding indices m are 4, 6, 8, 14, 25, 27, 29, 31 (A181978).

%C Note that values of d = p(m+1) - p(m-1) are multiples of 6.

%H Harvey P. Dale, <a href="/A181938/b181938.txt">Table of n, a(n) for n = 1..1000</a>

%e 7 = p(4) = 1 mod 6 and both p(3) = 5 and p(5) = 11 are congruent to 5 mod 6,

%e 13 = p(6) = 1 mod 6 and both p(5) = 11 and p(7) = 17 are congruent to 5 mod 6,

%e 43 = p(14) = 1 mod 6 and both p(13) = 41 and p(15) = 47 are congruent to 5 mod 6.

%t Select[Prime[Range[2, 300]], Mod[#, 6] == 1 && Mod[NextPrime[#, -1], 6] == 5 && Mod[NextPrime[#, 1], 6] == 5 &] (* _T. D. Noe_, Apr 04 2012 *)

%t Transpose[Select[Partition[Prime[Range[250]],3,1],Mod[#[[1]],6] == Mod[#[[3]],6] == 5&&Mod[#[[2]],6]==1&]][[2]] (* _Harvey P. Dale_, Sep 17 2012 *)

%Y Cf. A002476, A039704, A055625, A181978, A210248.

%K nonn

%O 1,1

%A _Zak Seidov_, Apr 03 2012