cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A306102 Numbers that are the difference of two positive squares in at least two ways.

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%I A306102 #21 Jul 11 2018 05:32:48
%S A306102 15,21,24,27,32,33,35,39,40,45,48,51,55,56,57,60,63,64,65,69,72,75,77,
%T A306102 80,81,84,85,87,88,91,93,95,96,99,104,105,108,111,112,115,117,119,120,
%U A306102 123,125,128,129,132,133,135,136,140,141,143,144,145,147,152,153,155,156
%N A306102 Numbers that are the difference of two positive squares in at least two ways.
%C A306102 Numbers n such that A100073(n) >= 2; see there for more information and formulas.
%C A306102 In sequence A058957 the smaller square is allowed to be zero, therefore it lists all squares > 4 (m^2 - 0^2 = ((m^2+1)/2)^2 - ((m^2-1)/2)^2 if odd, = (m^2/4+1)^2 - (m^2/4-1)^2 if even) in addition to the terms given here, which already comprise squares (64, 144, ...) having more representations than these "trivial" ones. - _M. F. Hasler_, Jul 11 2018
%H A306102 Geoffrey Campbell, <a href="https://www.linkedin.com/groups/4510047/4510047-6421706912643014658">Numbers that are the difference of two squares in two or more ways</a>, Number Theory group on LinkedIn, July 8, 2018.
%F A306102 A306102 = { n = 2k+1 | A056924(n) > 1 } U { n = 4k | A056924(n/4) > 1 }. - _M. F. Hasler_, Jul 10 2018
%t A306102 Select[Range@156, Length@ FindInstance[x^2 - y^2 == # && x>y>0, {x,y}, Integers, 2] == 2 &] (* _Giovanni Resta_, Jul 10 2018 *)
%o A306102 (PARI) select( is(n)=A100073(n)>1, [1..200]) \\ _M. F. Hasler_, Jul 10 2018
%Y A306102 Cf. A100073, A058957, A056924, A000290.
%Y A306102 Contains A306103 and A306104 as subsequences.
%K A306102 nonn
%O A306102 1,1
%A A306102 Geoffrey B. Campbell (Geoffrey.Campbell(AT)anu.edu.au), Jul 10 2018