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

1,1

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

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 *)

Crossrefs

Cf. A000040, A298866, A298867.

Sequence in context: A066680 A346635 A359159 * A211777 A189299 A028780

Adjacent sequences: A298862 A298863 A298864 * A298866 A298867 A298868

Keyword

nonn,easy

Author

Clark Kimberling, Feb 13 2018

Status

approved