A175620 -id:A175620 - cp's OEIS frontend

A173655 Triangle read by rows: T(n,k) = prime(n) mod prime(k), 0 < k <= n.

0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 1, 2, 1, 4, 0, 1, 1, 3, 6, 2, 0, 1, 2, 2, 3, 6, 4, 0, 1, 1, 4, 5, 8, 6, 2, 0, 1, 2, 3, 2, 1, 10, 6, 4, 0, 1, 2, 4, 1, 7, 3, 12, 10, 6, 0, 1, 1, 1, 3, 9, 5, 14, 12, 8, 2, 0, 1, 1, 2, 2, 4, 11, 3, 18, 14, 8, 6, 0, 1, 2, 1, 6, 8, 2, 7, 3, 18, 12, 10, 4, 0

Offset: 1

Juri-Stepan Gerasimov, Nov 24 2010

			Triangle begins as:
  0;
  1, 0;
  1, 2, 0;
  1, 1, 2, 0;
  1, 2, 1, 4, 0;
  1, 1, 3, 6, 2,  0;
  1, 2, 2, 3, 6,  4,  0;
  1, 1, 4, 5, 8,  6,  2,  0;
  1, 2, 3, 2, 1, 10,  6,  4, 0;
  1, 2, 4, 1, 7,  3, 12, 10, 6, 0;

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

Cf. A001223 (2nd diagonal), A033955 (row sums), A102647 (row products excluding 0's), A031131 (3rd diagonal after first 3 terms).

Cf. A172662, A174497, A174947, A174996, A175620.

A173655:= func< n,k | NthPrime(n) mod NthPrime(k) >;
[A173655(n,k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 10 2024

A173655 := proc(n,k) ithprime(n) mod ithprime(k) ;end proc:
seq(seq(A173655(n,k),k=1..n),n=1..20) ; # R. J. Mathar, Nov 24 2010

Flatten[Table[Mod[Prime[n], Prime[Range[n]]], {n, 15}]]

forprime(p=2,40,forprime(q=2,p,print1(p%q", "))) \\ Charles R Greathouse IV, Dec 21 2011

def A173655(n,k): return nth_prime(n)%nth_prime(k)
flatten([[A173655(n,k) for k in range(1,n+1)] for n in range(1,13)]) # G. C. Greubel, Apr 10 2024

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

Original entry on oeis.org

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

A174947 Triangle read by rows: T(n,k) = (prime(n)+1) mod prime(k).

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 2, 3, 1, 0, 0, 2, 5, 1, 0, 2, 4, 0, 3, 1, 0, 0, 3, 4, 7, 5, 1, 0, 2, 0, 6, 9, 7, 3, 1, 0, 0, 4, 3, 2, 11, 7, 5, 1, 0, 0, 0, 2, 8, 4, 13, 11, 7, 1, 0, 2, 2, 4, 10, 6, 15, 13, 9, 3, 1, 0, 2, 3, 3, 5, 12, 4, 0, 15, 9, 7, 1, 0, 0, 2, 0, 9, 3, 8, 4, 19, 13, 11, 5, 1, 0, 2, 4, 2, 0, 5, 10, 6, 21, 15, 13, 7, 3, 1

Offset: 1

Juri-Stepan Gerasimov, Dec 02 2010

Triangle read by rows: T(n,k) = Sigma(prime(n)) mod prime(k), where Sigma(prime(.)) is the sum of divisors of prime.

			Triangle begins
  1;
  0, 1;
  0, 0, 1;
  0, 2, 3, 1;
  0, 0, 2, 5, 1;
  0, 2, 4, 0, 3,  1;
  0, 0, 3, 4, 7,  5,  1;
  0, 2, 0, 6, 9,  7,  3,  1;
  0, 0, 4, 3, 2, 11,  7,  5, 1;
  0, 0, 0, 2, 8,  4, 13, 11, 7, 1;

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

Cf. A174428, A173655, A173662, A174996, A175620, A177226.

[(1+NthPrime(n)) mod NthPrime(k): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 10 2024

Table[Mod[1+Prime[n], Prime[k]], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Apr 10 2024 *)

trga(nrows) = {for (n=1, nrows, for (k=1, n, print1(sigma(prime(n)) % prime(k), ", ");); print(););} \\ Michel Marcus, Apr 11 2013

flatten([[(1+nth_prime(n))%nth_prime(k) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 10 2024

Corrected by D. S. McNeil, Dec 02 2010

cp's OEIS Frontend

A173655 Triangle read by rows: T(n,k) = prime(n) mod prime(k), 0 < k <= n.

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

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A174947 Triangle read by rows: T(n,k) = (prime(n)+1) mod prime(k).

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Programs

Magma

Mathematica

PARI

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