OFFSET
1,3
COMMENTS
Sequence includes arbitrarily large values as well as infinitely many 1s.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..20000
R. P. Bambah and S. Chowla, On numbers which can be expressed as a sum of two squares. Proc. Nat. Inst. Sci. India (1947), 101-103.
Rainer Dietmann, Christian Elsholtz, Alexander Kalmynin, Sergei Konyagin, James Maynard, Longer Gaps Between Values of Binary Quadratic Forms, International Mathematics Research Notices, Volume 2023, Issue 12, June 2023, Pages 10313-10349.
P. Erdös, Some problems and results in elementary number theory, Publ. Math. Debrecen (1951), 103-109.
Ian Richards, On the gaps between numbers which are sums of two squares, Adv. in Math. (1982), 1-2.
MAPLE
b:= proc(n) option remember; local j, k;
for k from 1+`if`(n=1, -1, b(n-1)) do
for j from 0 to isqrt(iquo(k, 2)) do
if issqr(k-j^2) then return k fi
od od
end:
a:= n-> b(n+1)-b(n):
seq(a(n), n=1..100); # Alois P. Heinz, Mar 29 2015
MATHEMATICA
Select[Range[0, 1000], SquaresR[2, #] != 0&] // Differences (* Jean-François Alcover, Mar 28 2017 *)
PROG
(PARI) issum2sq(n) = my(fm=factor(n)); for(k=1, matsize(fm)[1], if(fm[k, 1]%4==3&&fm[k, 2]%2==1, return(0))); 1
al(n) = my(r=vector(n), j=0, k=0, last=0); while(k<n, if(issum2sq(j++), r[k++]=j-last; last=j)); r
(PARI) show(lim)=my(v=vectorsmall(lim\=1), u=List(), t=1); for(m=1, sqrtint(lim), for(n=1, sqrtint(lim-m^2), v[m^2+n^2]=1)); for(i=2, #v, if(v[i], listput(u, i-t); t=i)); Vec(u) \\ Charles R Greathouse IV, Mar 31 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Franklin T. Adams-Watters, Mar 28 2015
STATUS
approved