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Primes of the form A124080 (10 times triangular numbers) +- 1.
2

%I #6 Oct 31 2013 12:17:42

%S 11,29,31,59,61,101,149,151,211,281,359,449,659,661,911,1049,1051,

%T 1201,1361,1531,1709,1901,2099,2309,2311,2531,2999,3001,3251,3511,

%U 3779,4349,4649,4651,5279,5281,6299,6301,6659,6661,7411,8609,9029,9461,9901,11279

%N Primes of the form A124080 (10 times triangular numbers) +- 1.

%C Numbers j such that A124080(j)-1 is prime or A124080(j)+1 is prime, where repetition means a twin prime, are 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 11, 11, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 21, 22, 24, 24, 25, ..., . - _Robert G. Wilson v_, Nov 29 2006

%F {A124080(j)-1 when prime} U {A124080(j)+1 when prime} = {i = 10*T(j)-1 such that i is prime} U {i = 10*T(j)+1 such that i is prime} where T(j) = A000217(j) = j*(j+1)/2.

%e a(1) = A124080(1)+1 = (10*T(1)) - 1 = 10*(1*(1+1)/2) + 1 = 10+1 = 11 is prime.

%e a(2) = A124080(2)-1 = (10*T(2))-1 = 10*(2*(2+1)/2) - 1 = 30-1 = 29 is prime.

%e a(3) = A124080(2)+1 = (10*T(2))+1 = 10*(2*(2+1)/2) + 1 = 30+1 = 31 is prime.

%t s = {}; Do[t = 5n(n + 1); If[PrimeQ[t - 1], AppendTo[s, t - 1]]; If[PrimeQ[t + 1], AppendTo[s, t + 1]], {n, 47}]; s (* _Robert G. Wilson v_ *)

%Y Cf. A000040, A000217, A028895, A046092, A045943, A002378, A028896, A024966, A033996, A027468.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Nov 26 2006

%E More terms from _Robert G. Wilson v_, Nov 29 2006