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Triangle read by rows: T(n,k) = 2^(prime(n) - k - 1) mod n, 1 <= k <= n.
4

%I #23 Apr 13 2024 01:50:16

%S 0,0,1,2,1,2,0,0,0,0,2,1,3,4,2,2,4,2,4,2,4,1,4,2,1,4,2,1,0,0,0,0,0,0,

%T 0,0,8,4,2,1,5,7,8,4,2,8,4,2,6,8,4,2,6,8,4,6,3,7,9,10,5,8,4,2,1,6,8,4,

%U 8,4,8,4,8,4,8,4,8,4,8,4,2,1,7,10,5,9,11,12,6,3,8

%N Triangle read by rows: T(n,k) = 2^(prime(n) - k - 1) mod n, 1 <= k <= n.

%H Harvey P. Dale, <a href="/A175620/b175620.txt">Table of n, a(n) for n = 1..10000</a>

%e Triangle begins:

%e 0;

%e 0, 1;

%e 2, 1, 2;

%e 0, 0, 0, 0;

%e 2, 1, 3, 4, 2;

%e 2, 4, 2, 4, 2, 4;

%p A175620 := proc(n,k) modp(2^(ithprime(n)-k-1) ,n) ; end proc: # _R. J. Mathar_, Dec 14 2010

%t Flatten[Table[PowerMod[2,Prime[n]-k-1,n],{n,20},{k,n}]] (* _Harvey P. Dale_, Dec 10 2012 *)

%o (Magma)

%o [Modexp(2,NthPrime(n)-k-1,n): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Apr 12 2024

%o (SageMath)

%o flatten([[pow(2,nth_prime(n)-k-1,n) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Apr 12 2024

%Y Cf. A000079, A173655, A177226.

%K nonn,tabl

%O 1,4

%A _Juri-Stepan Gerasimov_, Dec 12 2010