A114920 Triangle where a(0,0) = 1; a(n,m) = number of terms in row (n-1) which, when added to m, are primes.

1, 0, 1, 0, 1, 2, 1, 2, 2, 2, 3, 4, 1, 3, 1, 2, 3, 4, 1, 4, 0, 2, 4, 3, 4, 2, 2, 1, 4, 6, 2, 5, 2, 3, 1, 2, 5, 6, 3, 4, 2, 4, 2, 2, 2, 6, 7, 2, 6, 1, 5, 1, 3, 2, 6, 5, 7, 4, 2, 4, 5, 4, 3, 2, 2, 4, 7, 7, 3, 7, 2, 3, 3, 4, 3, 7, 2, 3, 11, 3, 5, 3, 9, 2, 4, 1, 5, 3, 9, 2, 4, 8, 5, 9, 4, 6, 2, 4, 2, 8, 4, 6, 2, 4, 2

Offset

0,6

Links

Michael De Vlieger, Table of n, a(n) for n = 0..11627 (rows 0 <= n <= 150).

Example

Row 3 of the triangle is [1,2,2,2]. Adding 0 to these gives [1,2,2,2], of which 3 terms are primes. Adding 1 to these gives [2,3,3,3], of which 4 terms are primes. Adding 2 to these gives [3,4,4,4], of which one term is prime. Adding 3 to these gives [4,5,5,5], of which 3 terms are primes. Adding 4 to these gives [5,6,6,6], of which one term is prime. So row 4 is [3,4,1,3,1].
Triangle begins:
  1;
  0, 1;
  0, 1, 2;
  1, 2, 2, 2;
  3, 4, 1, 3, 1;
  2, 3, 4, 1, 4, 0;
  2, 4, 3, 4, 2, 2, 1;
  ...

Mathematica

NestList[Function[w, Map[Function[k, Count[Map[k + # &, w], _?PrimeQ]], Range[0, Length@ w]]], {1}, 13] // Flatten (* Michael De Vlieger, Sep 07 2017 *)

Prog

(PARI) {v=[1]; for(k=1, 20, w=vector(length(v)+1); for(i=0, length(v), for(j=1, length(v), if(isprime(v[j]+i), w[i+1]++))); v=w; print(v))} \\ Lambert Herrgesell(zero815(AT)googlemail.com), Jan 13 2006

Crossrefs

Cf. A114919, A114905, A114906.

Sequence in context: A123505 A320779 A356876 * A283190 A030361 A060715

Adjacent sequences: A114917 A114918 A114919 * A114921 A114922 A114923

Keyword

nonn,tabl

Author

Leroy Quet, Jan 07 2006

Extensions

More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Jan 13 2006

Status

approved