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A374845
The numbers p or 2p with p prime and p = 3 mod 4, in ascending order.
1
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
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
KEYWORD
nonn
AUTHOR
Manfred Boergens, Jul 22 2024
STATUS
approved