A094191 a(n) = smallest positive number that occurs exactly n times as a difference between two positive squares.
3, 15, 45, 96, 192, 240, 576, 480, 720, 960, 12288, 1440, 3600, 3840, 2880, 3360, 20736, 5040, 147456, 6720, 11520, 14400, 50331648, 10080, 25920, 245760, 25200, 26880, 3221225472, 20160, 57600, 30240, 184320, 3932160, 103680, 40320, 129600, 2985984, 737280, 60480, 13194139533312, 80640, 9663676416, 430080, 100800, 251658240, 84934656, 110880, 921600, 181440
Offset: 1
Keywords
Examples
a(1)=3 because there is only one difference of positive squares which equals 3 (2^2-1^1). a(2)=15 because 15 = 4^2-1^2 = 8^2-7^2. a(3)=45 because 45 = 7^2-2^2 = 9^2-6^2 = 23^2-22^2.
Links
- T. D. Noe, Table of n, a(n) for n = 1..999
- Johan Claes, homepage. [Broken link (unknown server) replaced with link to current user's "homepage". - _M. F. Hasler_, Mar 14 2018]
Crossrefs
Cf. A068314.
Programs
-
Mathematica
s = Split[ Sort[ Flatten[ Table[ Select[ Table[ b^2 - c^2, {c, b - 1}], # < 500000 &], {b, 250000}]]]]; f[s_, p_] := Block[{l = Length /@ s}, If[ Position[l, p, 1, 1] != {}, d = s[[ Position[l, p, 1, 1][[1, 1]] ]] [[1]], d = 0]; d]; t = Table[ f[s, n], {n, 36}] (* Robert G. Wilson v, Jun 04 2004 *) -
PARI
{occurrences(d)=local(c,n,a);c=0;for(n=1,(d-1)\2,if(issquare(a=n^2+d),c++));c} {m=50;z=30000;v=vector(m,n,-1);for(d=1,z,k=occurrences(d);if(0
Extensions
Edited by Don Reble and Klaus Brockhaus, Jun 04 2004
Further terms from Johan Claes, Jun 07 2004
a(43) corrected by T. D. Noe, Mar 14 2018
Comments