A256435 First differences of sums of two squares.

1, 1, 2, 1, 3, 1, 1, 3, 3, 1, 1, 2, 5, 1, 3, 3, 2, 2, 1, 3, 1, 4, 4, 1, 2, 1, 5, 3, 3, 1, 3, 4, 1, 1, 6, 1, 1, 3, 4, 1, 7, 1, 2, 1, 3, 2, 3, 4, 3, 1, 4, 1, 3, 3, 2, 6, 1, 7, 1, 1, 2, 1, 4, 4, 3, 2, 2, 5, 1, 3, 5, 2, 1, 4, 8, 1, 2, 1, 3, 2, 3, 3, 4, 6, 3, 4, 1, 3, 3, 1, 1, 7, 1, 2, 1, 5, 6, 1, 3, 1

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

Formula

a(n) = A001481(n+1) - A001481(n).

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

Cf. A001481 (sums of 2 squares), A005408 (differences between squares).

Sequence in context: A006346 A244740 A088742 * A367412 A279945 A342724

Adjacent sequences: A256432 A256433 A256434 * A256436 A256437 A256438

Keyword

nonn

Author

Franklin T. Adams-Watters, Mar 28 2015

Status

approved