login
Primes such that the sum of the predecessor and successor primes is divisible by 11.
15

%I #9 Nov 21 2013 12:48:45

%S 31,43,67,109,131,139,191,617,727,881,911,937,953,991,1049,1289,1381,

%T 1429,1543,1571,1619,1657,1693,1721,1723,1777,1783,1871,1979,2251,

%U 2311,2341,2377,2441,2531,2579,2837,2953,3061,3221,3257,3557,3559,3631,3673

%N Primes such that the sum of the predecessor and successor primes is divisible by 11.

%F a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 11. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 11.

%e a(1) = 31 because prevprime(31) + nextprime(31) = 29 + 37 = 66 = 11 * 6.

%e a(2) = 43 because prevprime(43) + nextprime(43) = 41 + 47 = 88 = 11 * 8.

%e a(3) = 67 because prevprime(67) + nextprime(67) = 61 + 71 = 132 = 11 * 12.

%e a(4) = 109 because prevprime(109) + nextprime(109) = 107 + 113 = 220 = 11 * 20.

%t Prime@ Select[Range[2, 515], Mod[Prime[ # - 1] + Prime[ # + 1], 11] == 0 &] (* _Robert G. Wilson v_ *)

%t Transpose[Select[Partition[Prime[Range[550]],3,1],Divisible[First[#]+ Last[#], 11]&]][[2]] (* _Harvey P. Dale_, Jul 22 2011 *)

%Y Cf. A000040, A112681, A112794, 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 More terms from _Robert G. Wilson v_, Jan 05 2006