A217697 a(n) is the smallest positive integer such that 4n+2 can be partitioned into the sum of two primes in the form of 4k+3 in n ways.

1, 3, 12, 19, 28, 22, 37, 61, 58, 52, 67, 82, 124, 112, 148, 97, 175, 127, 214, 172, 157, 295, 280, 232, 217, 328, 331, 277, 247, 262, 520, 337, 388, 448, 430, 409, 382, 442, 367, 397, 610, 487, 412, 535, 547, 502, 592, 472, 703, 766, 652, 727, 637, 991, 802

Offset: 1

Author

Lei Zhou, Mar 19 2013

Keywords

• nonn

Comments

This is also the index of the first occurrence of n in A156642.

Examples

			a(3) = 12 because 50 = 4*12 + 2 is the smallest number of the form 4m + 2 which can be expressed as a sum of 2 primes of the form 4k + 3 in 3 ways (3 + 47, 7 + 43, and 19 + 31).
a(3) = 12 because A156642(12) = 3 while for 0<=n<12, A156642(n) < 3.
		

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A156642, A214834, A016825, A000040, A002145, A217696.

Programs

Mathematica

goal = 56; a = {}; Do[AppendTo[a, 0], {n, 1, goal}]; found = 0; k = 0; While[found < goal, k++; m = 4*k + 2; p1 = m + 1; ct = 0;
While[p1 = p1 - 4; p2 = m - p1; p1 >= p2, If[PrimeQ[p1] && PrimeQ[p2], ct++]]; If[ct <= goal, If[a[[ct]] == 0, a[[ct]] = k; found++]]]; a