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

1,1

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

Table of n, a(n) for n=1..64.

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

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]

Crossrefs

Cf. A374846, A292762, A046081.

Sequence in context: A047556 A255053 A292762 * A364927 A258233 A015819

Adjacent sequences: A374842 A374843 A374844 * A374846 A374847 A374848

Keyword

nonn

Author

Manfred Boergens, Jul 22 2024

Status

approved