A156074 Triangle read by rows: T(n, k) = 3 + prime(n+1) - prime(k+1) - prime(n-k+1).

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 4, 4, 1, 1, 2, 4, 4, 2, 1, 1, 4, 4, 6, 4, 4, 1, 1, 2, 4, 4, 4, 4, 2, 1, 1, 4, 4, 6, 4, 6, 4, 4, 1, 1, 6, 8, 8, 8, 8, 8, 8, 6, 1, 1, 2, 6, 8, 6, 8, 6, 8, 6, 2, 1, 1, 6, 6, 10, 10, 10, 10, 10, 10, 6, 6, 1, 1, 4, 8, 8, 10, 12, 10, 12, 10, 8, 8, 4, 1

Offset

0,5

Comments

Row sums are: {1, 2, 4, 6, 14, 14, 24, 22, 34, 62, 54, ...}.

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

T(n, k) = 3 + prime(n+1) - prime(k+1) - prime(n-k+1).

Example

Triangle begins as:
  1;
  1, 1;
  1, 2, 1;
  1, 2, 2, 1;
  1, 4, 4, 4, 1;
  1, 2, 4, 4, 2, 1;
  1, 4, 4, 6, 4, 4, 1;
  1, 2, 4, 4, 4, 4, 2, 1;
  1, 4, 4, 6, 4, 6, 4, 4, 1;
  1, 6, 8, 8, 8, 8, 8, 8, 6, 1;
  1, 2, 6, 8, 6, 8, 6, 8, 6, 2, 1;

Maple

seq(seq( 3+ ithprime(n+1) -ithprime(k+1) -ithprime(n-k+1), k=0..n), n=0..15); # G. C. Greubel, Dec 02 2019

Mathematica

Table[3 +Prime[n+1] -Prime[k+1] -Prime[n-k+1], {n, 0, 15}, {k, 0, n}]//Flatten

Prog

(PARI) T(n, k) = 3 + prime(n+1) - prime(k+1) - prime(n-k+1); \\ G. C. Greubel, Dec 02 2019
(Magma) P:=NthPrime; [3 +P(n+1) -P(k+1) -P(n-k+1): k in [0..n], n in [0..15]]; // G. C. Greubel, Dec 02 2019
(Sage) p=nth_prime; [[3 +p(n+1) -p(k+1) -p(n-k+1) for k in (0..n)] for n in (0..15)] # G. C. Greubel, Dec 02 2019

Crossrefs

Sequence in context: A342767 A176653 A174842 * A051287 A278218 A216031

Adjacent sequences: A156071 A156072 A156073 * A156075 A156076 A156077

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 03 2009

Extensions

More terms added by G. C. Greubel, Dec 02 2019

Status

approved