A026468 -id:A026468 - cp's OEIS frontend

A026469 a(1) = 1; for n > 1, a(n) = least positive integer > a(n-1) and not equal to a(i)^2 + a(j)^2 for 1<=i<=j<=n-1.

1, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 33, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 68, 69, 70, 71, 75, 76, 77, 78, 79

Offset: 1

Clark Kimberling

nonn

A022544 is a subsequence.

Cf. A026468.

# 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:
A026469 := proc(nmax) local a,candidat ; a := [1] ; 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: A026469(60) ; # R. J. Mathar, Nov 01 2006

Corrected by Franklin T. Adams-Watters, Oct 25 2006

Definition corrected by N. J. A. Sloane, Nov 01 2006

A008320 Smallest number that is not the sum of squares of two distinct earlier terms.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 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, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 81, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94

Offset: 1

R. Muller

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000
Mihaly Bencze [Beneze], Smarandache Recurrence Type Sequences, Unknown source, pp. 99-102. Originally appeared in Bull. Pure Appl. Sciences.
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
Eric Weisstein's World of Mathematics, Smarandache Sequences.

A026468 is the version without "distinct".

FixedPoint[Complement[Range@100, Flatten@Table[#[[i]]^2 + #[[j]]^2, {i, Length[#]}, {j, i - 1}]] &, {}] (* Ivan Neretin, Jun 05 2016 *)

More terms from David W. Wilson

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

A026469 a(1) = 1; for n > 1, a(n) = least positive integer > a(n-1) and not equal to a(i)^2 + a(j)^2 for 1<=i<=j<=n-1.

Views

Author

Keywords

Crossrefs

Programs

Maple

Extensions

A008320 Smallest number that is not the sum of squares of two distinct earlier terms.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula