A026469 -id:A026469 - cp's OEIS frontend

A026468 a(1) = 1, a(2) = 2; for n >= 3, a(n) = least positive integer > a(n-1) and not a(i)^2 + a(j)^2 for 1<=i<=j<=n-1.

1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 15, 16, 19, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78

Offset: 1

Clark Kimberling

nonn

A022544 is a subsequence.

Cf. A026469, A261604.

# return true if 'candid' is allowed (not a sum of squares)
A026469aux := proc(a,candid) local i,j; for j from 1 to nops(a) do for i from 1 to j do if (op(i,a))^2+(op(j,a))^2 = candid then RETURN(false); fi; od; od; RETURN(true); end:
A026468 := proc(nmax) local a,candidat; a := [1,2]; while nops(a) < nmax do candidat := op(nops(a),a)+1; while A026469aux(a,candidat) = false do candidat := candidat+1; od; a := [op(a),candidat]; od: RETURN(a); end: A026468(60); # R. J. Mathar, Nov 01 2006

Definition corrected by Ralf Stephan, Nov 01 2006

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

Original entry on oeis.org

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

Anders Hellström, Aug 25 2015

nonn

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

A022544 is a subsequence.

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

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;

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

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

cp's OEIS Frontend

A026468 a(1) = 1, a(2) = 2; for n >= 3, a(n) = least positive integer > a(n-1) and not a(i)^2 + a(j)^2 for 1<=i<=j<=n-1.

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