# new sequence from Hardy Collected papers.

Simon Plouffe plouffe at math.uqam.ca
Sat Aug 1 18:27:29 CEST 1998

```I found this one in Hardy's Collected Papers, Volume 1, page 466.

%I A000000
%S A000000 4,16,5,9,4,32,13,12,11,16,6,14,15,64,6,27,4,25,24,23,23,
%T A000000 32,10,26,40,29,29,30,5,128
%N A000000 Minimal solution of a congruence.
%R A000000 HAR 1 466.
%O A000000 3,1
%K A000000 nonn
%A A000000 Simon Plouffe (plouffe at math.uqam.ca).
%H A000000
%D A000000
%p A000000
- ---------------------------------------------------------------------------

%R more precisely (in case of mistake).

G.H. Hardy , Collected Papers, Volume 1, 1966 Oxford University Press, page 466.

The exact description of that sequence is (somehat long),

"Let G(k) be the smallest integer s such that for all n and all primes p,
and all m>0 the congruence

(x_1)^k + ... + (x_s)^k congruent to s (mod p^n)

has a solution in which not all the (x_i) are all congruent to 0 (mod p)".

So the sequence is G(k) (G for Gamma(k) in the paper).

Simon Plouffe

```