|
| |
|
|
A094191
|
|
a(n) = smallest positive number that occurs exactly n times as a difference between two positive squares.
|
|
3
|
|
|
|
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
|
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
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
