A112794 - OEIS

%I #12 May 18 2019 18:27:32

%S 5,11,19,41,71,73,89,97,101,109,137,149,181,229,241,281,293,311,349,

%T 359,389,397,409,419,421,433,449,457,461,487,541,557,587,631,701,709,

%U 743,751,787,811,859,881,887,919,937,991,997,1009,1021,1033,1049,1051,1063

%N Primes such that the sum of the predecessor and successor primes is divisible by 5.

%H Harvey P. Dale, <a href="/A112794/b112794.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 5. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 5.

%e a(1) = 5 because prevprime(5) + nextprime(5) = 3 + 7 = 10 = 5 * 2.

%e a(2) = 11 because prevprime(11) + nextprime(11) = 7 + 13 = 20 = 5 * 4.

%e a(3) = 19 because prevprime(19) + nextprime(19) = 17 + 23 = 40 = 5 * 8.

%e a(4) = 41 because prevprime(41) + nextprime(41) = 37 + 43 = 80 = 5 * 16.

%t Prime@ Select[Range[2, 179], Mod[Prime[ # - 1] + Prime[ # + 1], 5] == 0 &] (* _Robert G. Wilson v_ *)

%t Select[Partition[Prime[Range[200]],3,1],Divisible[#[[1]]+#[[3]],5]&] [[All,2]] (* _Harvey P. Dale_, May 18 2019 *)

%Y Cf. A000040, A112681, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jan 01 2006

%E Corrected and extended by _Robert G. Wilson v_, Jan 05 2006