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A049763 Triangular array T, read by rows: T(n,k) = n^4 mod k, for k = 1..n and n >= 1. 4

%I #19 Sep 08 2022 08:44:58

%S 0,0,0,0,1,0,0,0,1,0,0,1,1,1,0,0,0,0,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,4,

%T 1,0,0,1,0,1,1,3,2,1,0,0,0,1,0,0,4,4,0,1,0,0,1,1,1,1,1,4,1,7,1,0,0,0,

%U 0,0,1,0,2,0,0,6,1,0,0,1,1,1,1,1

%N Triangular array T, read by rows: T(n,k) = n^4 mod k, for k = 1..n and n >= 1.

%H G. C. Greubel, <a href="/A049763/b049763.txt">Rows n = 1..100 of triangle, flattened</a>

%e Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:

%e 0;

%e 0, 0;

%e 0, 1, 0;

%e 0, 0, 1, 0;

%e 0, 1, 1, 1, 0;

%e 0, 0, 0, 0, 1, 0;

%e 0, 1, 1, 1, 1, 1, 0;

%e 0, 0, 1, 0, 1, 4, 1, 0;

%e 0, 1, 0, 1, 1, 3, 2, 1, 0;

%e 0, 0, 1, 0, 0, 4, 4, 0, 1, 0;

%e ...

%p seq(seq( `mod`(n^4, k), k = 1..n), n = 1..20); # _G. C. Greubel_, Dec 13 2019

%t Flatten[Table[PowerMod[n,4,k],{n,20},{k,n}]] (* _Harvey P. Dale_, Jan 19 2015 *)

%o (PARI) T(n,k) = lift(Mod(n,k)^4);

%o for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Dec 13 2019

%o (Magma) [[Modexp(n,4,k): k in [1..n]]: n in [1..15]]; // _G. C. Greubel_, Dec 13 2019

%o (Sage) [[power_mod(n,4,k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Dec 13 2019

%o (GAP) Flat(List([1..15], n-> List([1..n], k-> PowerMod(n,4,k) ))); # _G. C. Greubel_, Dec 13 2019

%Y Row sums are in A049764.

%Y Cf. A049759, A049760, A049761, A049762.

%K nonn,tabl

%O 1,34

%A _Clark Kimberling_

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)