A114919 Triangle where a(0,0) = 0; a(n,m) = number of terms in row (n-1) which, when added to m, are primes.

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

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 [1,1,2,3]. Adding 0 to these gives [1,1,2,3], of which 2 terms are primes. Adding 1 to these gives [2,2,3,4], of which 3 terms are primes. Adding 2 to these gives [3,3,4,5], of which 3 terms are primes. Adding 3 to these gives [4,4,5,6], of which 1 term is prime. Adding 4 to these gives [5,5,6,7], of which 3 terms are primes. So row 4 is [2,3,3,1,3].

Maple

A114919 := proc(rowmax) local a, n, m, t ; a := matrix(rowmax, rowmax) ; a[1, 1] := 0 ; for n from 2 to rowmax do for m from 1 to n do a[n, m] := 0 ; for t from 1 to n-1 do if isprime( m-1+a[n-1, t] ) then a[n, m] := a[n, m]+1 ; fi ; od ; od ; od ; RETURN(a) ; end: rowmax := 15 : a := A114919(rowmax) : for n from 1 to rowmax do for m from 1 to n do printf("%d, ", a[n, m]) ; od ; od ; # R. J. Mathar, Mar 13 2007

Mathematica

NestList[Function[w, Map[Function[k, Count[Map[k + # &, w], _?PrimeQ]], Range[0, Length@ w]]], {0}, 13] // Flatten (* Michael De Vlieger, Sep 06 2017 *)

Crossrefs

Cf. A114920, A114905, A114906.

Sequence in context: A205725 A091093 A049615 * A087917 A330334 A087741

Adjacent sequences: A114916 A114917 A114918 * A114920 A114921 A114922

Keyword

nonn,tabl

Author

Leroy Quet, Jan 07 2006

Extensions

More terms from R. J. Mathar, Mar 13 2007

Status

approved