A176066 -id:A176066 - cp's OEIS frontend

A174996 Triangle read by rows: T(n,k) = (prime(n)-1) mod prime(k).

1, 0, 2, 0, 1, 4, 0, 0, 1, 6, 0, 1, 0, 3, 10, 0, 0, 2, 5, 1, 12, 0, 1, 1, 2, 5, 3, 16, 0, 0, 3, 4, 7, 5, 1, 18, 0, 1, 2, 1, 0, 9, 5, 3, 22, 0, 1, 3, 0, 6, 2, 11, 9, 5, 28, 0, 0, 0, 2, 8, 4, 13, 11, 7, 1, 30, 0, 0, 1, 1, 3, 10, 2, 17, 13, 7, 5, 36, 0, 1, 0, 5, 7, 1, 6, 2, 17, 11, 9, 3, 40, 0, 0, 2, 0, 9, 3, 8, 4, 19, 13, 11, 5, 1, 42

Offset: 1

Juri-Stepan Gerasimov, Dec 02 2010

			The triangle starts in row n=0 with columns 1<=k<= n as:
  1;
  0, 2;
  0, 1, 4;
  0, 0, 1, 6;
  0, 1, 0, 3, 10;
  0, 0, 2, 5,  1, 12;
  0, 1, 1, 2,  5,  3, 16;
  0, 0, 3, 4,  7,  5,  1, 18;
  0, 1, 2, 1,  0,  9,  5,  3, 22;
  0, 1, 3, 0,  6,  2, 11,  9,  5, 28;

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Cf. A006093, A173655, A173662, A174428, A174947, A175620, A176066, A177226.

[(NthPrime(n)-1) mod NthPrime(k): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 12 2024

Flatten[Table[Mod[Prime[n]-1,Prime[k]],{n,15},{k,n}]]  (* Harvey P. Dale, Apr 23 2011 *)

flatten([[(nth_prime(n)-1)%nth_prime(k) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 12 2024

A177266 Triangle read by rows: R(n,k) = 2^(semiprime(n)-semiprime(k)) mod semiprime(n).

Original entry on oeis.org

1, 4, 1, 5, 8, 1, 4, 6, 2, 1, 2, 4, 4, 2, 1, 8, 2, 4, 2, 2, 1, 11, 8, 1, 11, 2, 1, 1, 14, 20, 8, 4, 14, 18, 2, 1, 2, 13, 11, 18, 23, 24, 16, 8, 1, 10, 22, 6, 16, 14, 20, 6, 16, 2, 1, 17, 29, 16, 8, 17, 25, 4, 2, 25, 29, 1, 30, 16, 2, 18, 16, 8, 32, 16, 2, 18, 2, 1, 23, 32, 4, 2, 22

Offset: 1

Juri-Stepan Gerasimov, Dec 10 2010

			Triangle begins:
1,
4, 1,
5, 8, 1,
4, 6, 2, 1,
2, 4, 4, 2, 1,
8, 2, 4, 2, 2, 1,

Cf. A000079, A001358, A173622, A174479, A176066, A181615.

Table[PowerMod[2, #[[n]] - #[[;;n]], #[[n]]], {n, Length[#]}] & [Select[Range[50], PrimeOmega[#] == 2 &]] (* Paolo Xausa, Jun 28 2024 *)

trg(nn) = {semip = select(n->bigomega(n) == 2, vector(nn, i, i)); for (n = 1, #semip, for (k = 1, n, print1(2^(semip[n] - semip[k]) % semip[n], ", ");); print(););} \\ Michel Marcus, Sep 11 2013

Corrected by D. S. McNeil, Dec 10 2010

cp's OEIS Frontend

A174996 Triangle read by rows: T(n,k) = (prime(n)-1) mod prime(k).

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