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

1,2

Comments

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

Links

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

Example

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.

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

Crossrefs

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

Sequence in context: A120623 A158517 A043877 * A134965 A117554 A049714

Adjacent sequences: A217694 A217695 A217696 * A217698 A217699 A217700

Keyword

nonn

Author

Lei Zhou, Mar 19 2013

Status

approved