A177226 - OEIS

%I #16 Apr 10 2024 03:32:49

%S 1,2,1,3,4,1,4,2,4,1,6,3,9,5,1,7,10,9,12,4,1,9,13,16,4,13,16,1,10,5,6,

%T 11,9,7,4,1,12,6,13,9,2,12,18,16,1,15,22,20,5,13,25,7,9,6,1,16,8,2,16,

%U 1,8,16,4,8,4,1,19,28,7,11,3,10,33,36,30,34,27,1,21,31,18,25,40,10,16,4,31,37,40,16,1

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

%H G. C. Greubel, <a href="/A177226/b177226.txt">Rows n = 1..50 of the triangle, flattened</a>

%F From _G. C. Greubel_, Apr 09 2024: (Start)

%F T(n, 1) = A111333(n).

%F T(n, 2) = A292411(n). (End)

%e Triangle begins:

%e    1;

%e    2,  1;

%e    3,  4,  1;

%e    4,  2,  4,  1;

%e    6,  3,  9,  5,  1;

%e    7, 10,  9, 12,  4,  1;

%e    9, 13, 16,  4, 13, 16,  1;

%e   10,  5,  6, 11,  9,  7,  4,  1;

%e   12,  6, 13,  9,  2, 12, 18, 16,  1;

%t Flatten[Table[PowerMod[2,Prime[n]-Prime[k],Prime[n]],{n,20},{k,n}]] (* _Harvey P. Dale_, May 10 2014 *)

%o (Magma)

%o A177226:= func< n,k | Modexp(2, NthPrime(n) - NthPrime(k), NthPrime(n)) >;

%o [A177226(n,k): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Apr 09 2024

%o (SageMath)

%o def A177226(n,k): return pow(2, nth_prime(n) - nth_prime(k), nth_prime(n))

%o flatten([[A177226(n,k) for k in range(1,n+1)] for n in range(1,13)]) # _G. C. Greubel_, Apr 09 2024

%Y Cf. A000079, A111333, A173655, A174497, A174947, A174996, A292411.

%K nonn,tabl

%O 1,2

%A _Juri-Stepan Gerasimov_, Dec 10 2010

%E Corrected by _D. S. McNeil_, Dec 10 2010