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.
Thomas Bloom, Problem 222, Erdős Problems.
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.
Paul Erdös, Some problems and results in elementary number theory, Publ. Math. Debrecen (1951), 103-109.
Erdős problems database contributors, Erdős problem database, see no. 222.
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