A258713 A001172(n)/2: Least k such that 2k is a sum of two odd primes in exactly n ways.

0, 3, 5, 11, 17, 24, 30, 39, 42, 45, 57, 72, 60, 84, 90, 117, 123, 144, 120, 105, 162, 150, 180, 237, 165, 264, 288, 195, 231, 240, 210, 285, 255, 336, 396, 378, 438, 357, 399, 345, 519, 315, 504, 465, 390, 480, 435, 462, 450, 567, 717, 420, 495, 651

Offset: 0

Author

N. J. A. Sloane, Jun 14 2015

Keywords

• nonn

Comments

Up to a(14) also indices of records in A002375, number of ways to write 2n as sum of two odd primes. - M. F. Hasler, Aug 21 2017

Links

• Robert Israel, Table of n, a(n) for n = 0..845

Crossrefs

Cf. A136244, A001172.

Cf. A002375, A002372, A045917.

Programs

Maple

g:= add(x^ithprime(i),i=2..1000):
G:= series((g^2+add(x^(2*ithprime(i)),i=2..1000))/2,x,ithprime(1001)+3):
A[0]:= 0:
for k from 1 to (ithprime(1001)+1)/2 do
  m:= coeff(G,x,2*k);
  if not assigned(A[m]) then A[m]:= k fi;
od:
for m from 1 while assigned(A[m]) do od:
seq(A[i],i=0..m-1); # Robert Israel, Aug 21 2017

Mathematica

With[{s = Array[Count[Select[IntegerPartitions[2 #, 2], Length@ # == 2 &], p_ /; AllTrue[p, And[PrimeQ@ #, OddQ@ #] &]] &, 10^3]}, Table[FirstPosition[s, n][[1]] /. 1 -> 0, {n, 0, 53}]] (* Michael De Vlieger, Aug 21 2017 *)

Extensions

Edited by M. F. Hasler, Aug 21 2017

Edited by Robert Israel, Aug 21 2017