A261604 a(1)=0. For n>1, a(n) = smallest number > a(n-1) such that, for all m,r

0, 1, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 33, 35, 38, 39, 40, 42, 43, 44, 46, 47, 48, 51, 53, 54, 55, 56, 57, 59, 60, 62, 63, 66, 67, 68, 69, 70, 71, 75, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88

Offset: 1

Author

Anders Hellström, Aug 25 2015

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Anders Hellström, Ruby program

Crossrefs

A022544 is a subsequence.

Cf. A026468, A026466, A026467, A026469, A026470.

Programs

PARI

issumsq(n,r,s)=(r^2)+(s^2)==n
first(m)=my(v=vector(m), x, r, n, s); v[1]=0; for(n=2, m, v[n]=v[n-1]+1;until(x==1, for(r=1, n-1, for(s=1, n-1, if(issumsq(v[n],v[r],v[s]), v[n]++; x=0; break(2), x=1))))); v;

PARI

isA022544(n)=if(n%4==3, return(1)); my(f=factor(n)); for(i=1,#f~, if(f[i,1]%4==3 && f[i,2]%2, return(1))); 0
search(v,x)=my(t=setsearch(v,x)); if(t, t, setsearch(v,x,1))
list(lim)=my(v=List([0,1]),t); for(n=3,lim, if(isA022544(n), listput(v,n); next); for(j=search(v,sqrtint((n-1)\2)+1),search(v,sqrtint(n)), if(issquare(n-v[j]^2, &t) && setsearch(v,t), next(2))); listput(v,n)); Set(v) \\ Charles R Greathouse IV, Sep 01 2015

Formula

a(n) ~ n, and in particular a(n) = n + O(n/sqrt(log n)). I do not know if this bound is tight. - Charles R Greathouse IV, Sep 01 2015