A298865 The primes p and products 4*p in increasing order.

2, 3, 5, 7, 8, 11, 12, 13, 17, 19, 20, 23, 28, 29, 31, 37, 41, 43, 44, 47, 52, 53, 59, 61, 67, 68, 71, 73, 76, 79, 83, 89, 92, 97, 101, 103, 107, 109, 113, 116, 124, 127, 131, 137, 139, 148, 149, 151, 157, 163, 164, 167, 172, 173, 179, 181, 188, 191, 193

Offset: 1

Author

Clark Kimberling, Feb 13 2018

Keywords

• nonn
• easy

Comments

Conjecture: except for the first term, these are the nonsquares n for which there is a unique pair (x,y) such that x^2 - y^2 = n and x > y >= 0; see A257408.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A298866, A298867.

Programs

Mathematica

z = 10000; u = Prime[Range[z]]; w = Take[Union[u, 4 u], z]; (* A298865 *)
p[n_] := If[MemberQ[u, w[[n]]], 0, 1];
t = Table[p[n], {n, 1, z}];
Flatten[Position[t, 0]];  (* A298866 *)
Flatten[Position[t, 1]];  (* A298867 *)