%I #8 Mar 05 2024 14:42:28

%S 12,30,138,192,462,660,822,1092,1722,2028,2082,2712,3360,3540,3918,

%T 6132,6762,7590,7878,7950,8220,9462,9858,11352,12108,12378,13692,

%U 13998,14448,16140,16230,17292,17418,17580,18912,19470,19542,19992,20550,20748

%N Average of twin-prime pairs for pairs that are expressible as the sum of two triangular numbers.

%e a(1) = 12 as witnessed by 11 = 1 + 10 and 13 = 3 + 10;

%e a(5) = 462 as witnessed by 461 = 55 + 406 and 463 = 28 + 435.

%t s = Select[Union@ Flatten@ Table[i(i + 1)/2 + j(j + 1)/2, {i, 200}, {j, 0, i}], PrimeQ@ # &]; t = Select[Range@ Length@s - 1, s[[ # ]] + 2 == s[[ # + 1]] &]; s[[t]] + 1 (* _Robert G. Wilson v_, Apr 27 2006 *)

%Y Cf. A001097, A117048, A117112.

%K easy,nonn

%O 1,1

%A _Greg Huber_, Apr 24 2006

%E More terms from _Robert G. Wilson v_, Apr 27 2006