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
Keywords
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
- Anders Hellström, Ruby program
Programs
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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;
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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