A135203 For any integer n >= 1 the sequence gives the minimum power x for which n^x+(n-1)^x+(n-2)^x+...+1^x produces a perfect square.

1, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset

1,2

Comments

All 3's apart from 1's in positions given by A001108 and 2 for n=24.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

n=4 -> 4^3+3^3+2^3+1^3 = 64+27+8+1 = 100
n=5 -> 5^3+4^3+3^3+2^3+1^3 = 125+64+27+8+1 = 225
n=6 -> 6^3+5^3+4^3+3^3+2^3+1^3 = 216+125+64+27+8+1 = 441

Maple

P:=proc(n) local a, i, k, j, ok, x; for i from 1 by 1 to n do x:=1; ok:=1; while ok=1 do a:=0; k:=i; while k>0 do a:=a+k^x; k:=k-1; od; if (trunc(sqrt(a)))^2=a then print(x); ok:=0; else x:=x+1; fi; od; od; end: P(100);

Prog

(PARI) A135203(n) = for(x=1, oo, if(issquare(sum(k=1, n, k^x)), return(x))); \\ Antti Karttunen, Sep 27 2018

Crossrefs

Cf. A001108.

Sequence in context: A251551 A073139 A122845 * A251552 A379054 A324497

Adjacent sequences: A135200 A135201 A135202 * A135204 A135205 A135206

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 28 2007

Extensions

Offset and a typo in the definition corrected by Antti Karttunen, Sep 27 2018

Status

approved