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A094191 a(n) = smallest positive number that occurs exactly n times as a difference between two positive squares. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Related to A005179, "Smallest number with exactly n divisors", with which it shares a lot of common terms (in different positions).

It appears that, for entries having prime index p > 3, the minimal solution is 2^(p+1)*3 for Sophie Germain primes p.  The number 43 is not such a prime, and we have the smaller solution 2^30*3^2. - T. D. Noe, Mar 14 2018

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]

EXAMPLE

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.

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 *)

PROG

(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<k&&k<=m&&v[k]<0, v[k]=d)); for(n=1, m, print1(v[n], ", "))} \\ Klaus Brockhaus

CROSSREFS

Cf. A068314.

Sequence in context: A177146 A161400 A112810 * A050534 A048099 A030505

Adjacent sequences:  A094188 A094189 A094190 * A094192 A094193 A094194

KEYWORD

nonn

AUTHOR

Johan Claes, Jun 02 2004

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

STATUS

approved

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Last modified November 20 03:25 EST 2018. Contains 317371 sequences. (Running on oeis4.)