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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
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 (list; graph; refs; listen; history; text; internal format)
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 A324497 A179804

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

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Last modified April 17 02:26 EDT 2021. Contains 343059 sequences. (Running on oeis4.)