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A121084 Number of primitive Pythagorean-like triples a^2+b^2=c^2+k for k=2 with 0<c<=10^n. 3
1, 10, 100, 983, 9912, 99211, 991714 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

a(1)=1 because there is one solution (a,b,c) as (3,3,4) with 0<c<=10^1.

MATHEMATICA

Courtesy of Daniel Lichtblau of Wolfram Research: countTriples[m_, k_] := Module[ {c2, c2odd, total = 0, fax, g}, Do[ c2 = c^2 + k; If[c2 < 2, Continue[]]; c2odd = c2; While[EvenQ[c2odd], c2odd /= 2]; If [c2odd==1, If [OddQ[Log[2, c2]], total++ ]; Continue[]]; If[Mod[c2odd, 4] == 3, Continue[]]; g = GCD[c2odd, 100947]; If[g != 1 && g^2 != GCD[c2odd, 10190296809], Continue[]]; fax = Map[{Mod[ #[[1]], 4], #[[2]]}&, FactorInteger[c2odd]]; If[Apply[Or, Map[ #[[1]] == 3 && OddQ[ #[[2]]] &, fax]], Continue []]; fax = Cases[fax, {1, aa_}:>aa+1]; fax = Ceiling[Apply[Times, fax]/2]; total += fax; , {c, m}]; total]

CROSSREFS

Cf. A101931.

Sequence in context: A136858 A334612 A125948 * A272501 A171284 A125897

Adjacent sequences:  A121081 A121082 A121083 * A121085 A121086 A121087

KEYWORD

nonn

AUTHOR

Tito Piezas III, Aug 11 2006

EXTENSIONS

First few terms found by Tito Piezas III, James Waldby (j-waldby(AT)pat7.com). Subsequent terms found by Andrzej Kozlowski (akoz(AT)mimuw.edu.pl), Daniel Lichtblau (danl(AT)wolfram.com).

a(7) from Max Alekseyev, May 30 2007

STATUS

approved

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Last modified January 28 17:05 EST 2022. Contains 350657 sequences. (Running on oeis4.)