A124110 Primes of the form A124080 (10 times triangular numbers) +- 1.

11, 29, 31, 59, 61, 101, 149, 151, 211, 281, 359, 449, 659, 661, 911, 1049, 1051, 1201, 1361, 1531, 1709, 1901, 2099, 2309, 2311, 2531, 2999, 3001, 3251, 3511, 3779, 4349, 4649, 4651, 5279, 5281, 6299, 6301, 6659, 6661, 7411, 8609, 9029, 9461, 9901, 11279

Offset: 1

Author

Jonathan Vos Post, Nov 26 2006

Keywords

• easy
• nonn

Comments

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

Examples

			a(1) = A124080(1)+1 = (10*T(1)) - 1 = 10*(1*(1+1)/2) + 1 = 10+1 = 11 is prime.
a(2) = A124080(2)-1 = (10*T(2))-1 = 10*(2*(2+1)/2) - 1 = 30-1 = 29 is prime.
a(3) = A124080(2)+1 = (10*T(2))+1 = 10*(2*(2+1)/2) + 1 = 30+1 = 31 is prime.
		

Crossrefs

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

Programs

Mathematica

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 *)

Formula

{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.

Extensions

More terms from Robert G. Wilson v, Nov 29 2006