A374845 The numbers p or 2p with p prime and p = 3 mod 4, in ascending order.

3, 6, 7, 11, 14, 19, 22, 23, 31, 38, 43, 46, 47, 59, 62, 67, 71, 79, 83, 86, 94, 103, 107, 118, 127, 131, 134, 139, 142, 151, 158, 163, 166, 167, 179, 191, 199, 206, 211, 214, 223, 227, 239, 251, 254, 262, 263, 271, 278, 283, 302, 307, 311, 326, 331, 334, 347, 358, 359, 367, 379, 382, 383, 398

Offset: 1

Author

Manfred Boergens, Jul 22 2024

Keywords

• nonn

Comments

Numbers appearing exactly once in a Pythagorean triple and as the smallest number in this triple.

Subsequence of A292762.

Inserting 4 as second term gives A374846.

Links

• A. Tripathi, On Pythagorean triples containing a fixed integer, Fib. Q., 46/47 (2008/2009), 331-340. See Theorem 8.

Crossrefs

Cf. A374846, A292762, A046081.

Programs

Mathematica

t={}; Do[If[(PrimeQ[n]&&Mod[n, 4] == 3)||(PrimeQ[n/2]&&Mod[n/2, 4] == 3), t=Join[t,{n}]], {n, 470}]; t
(* Positions of the ones in  A046081, omitting position = 4;  based on program by Jean-François Alcover *)
a[1] = 0; a[n_] := Module[{f}, f = Select[FactorInteger[n], Mod[#[[1]], 4] == 1 &][[All, 2]]; (DivisorSigma[0, If[OddQ[n], n, n/2]^2] - 1)/2 + (Times @@ (2*f + 1) - 1)/2]; arr = Array[a, nmax]; fl = Flatten[Position[arr, 1]]; Delete[fl, 2]