A339652 a(n) is the least number k such that 2*k+1 has exactly n expressions as p+2*q where p and q are primes, or 0 if there is no such k.

1, 3, 4, 10, 8, 16, 22, 25, 37, 49, 55, 46, 52, 67, 76, 100, 82, 124, 115, 118, 160, 112, 136, 181, 205, 196, 142, 157, 235, 241, 217, 202, 232, 277, 340, 247, 391, 337, 436, 424, 481, 864, 292, 262, 448, 397, 520, 457, 367, 427, 595, 412, 382, 547, 487, 502, 517, 562, 655, 703, 598, 760, 592

Offset: 0

Author

J. M. Bergot and Robert Israel, Dec 13 2020

Keywords

• nonn

Comments

Conjecture: all a(n) > 0.

Examples

			a(4) = 8 because 2*8+1 = 17 has exactly 4 representations as p+2*q: 17 = 3 + 2*7 = 7 + 2*5 = 11 + 2*3 = 13 + 2*2, and this is not true for any k < 8.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..9400

Crossrefs

Cf. A046927, A339709.

Programs

Maple

# given table A046927
R:= Array(0..100):
for i from 0 to max(indices(A046927)) do
  v:= A046927[i];
  if R[v]= 0 then R[v]:= i fi
od:
seq(R[i],i=0..100);

PARI

f(n) = my(s); n=2*n+1; forprime(p=2, n\2, s+=isprime(n-2*p)); s;
a(n) = my(k=1); while(f(k) != n, k++); k; \\ Michel Marcus, Dec 14 2020

Formula

A046927(a(n)) = n if a(n) > 0.