A114905 Triangle where a(1,1) = 0; a(n,m) = number of terms in row (n-1) which, when added to m, are primes.

0, 0, 1, 1, 2, 1, 3, 2, 1, 2, 3, 2, 2, 2, 2, 4, 1, 4, 1, 4, 0, 5, 3, 4, 2, 1, 2, 4, 5, 3, 4, 2, 2, 2, 2, 2, 6, 2, 6, 1, 5, 1, 1, 2, 6, 8, 4, 2, 3, 5, 4, 3, 1, 2, 3, 5, 5, 5, 4, 3, 2, 2, 4, 5, 4, 3, 5, 6, 5, 2, 2, 4, 3, 6, 5, 2, 2, 4, 8, 4, 6, 1, 6, 3, 4, 4, 6, 1, 6, 3, 4, 10, 4, 5, 4, 5, 2, 8, 2, 5, 4, 5, 2, 8, 2

Offset

1,5

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11476 (rows 1 <= n <= 150).

Example

The third row is [1,2,1]. Adding m=3 to these terms gives [4,5,4], of which one number is prime. Therefore a[4,3]=1 in the next row, third column.
Triangle starts
0
0 1
1 2 1
3 2 1 2
3 2 2 2 2
4 1 4 1 4 0
5 3 4 2 1 2 4
5 3 4 2 2 2 2 2
6 2 6 1 5 1 1 2 6
8 4 2 3 5 4 3 1 2 3

Maple

A114905 := 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+a[n-1, t] ) then a[n, m] := a[n, m]+1 ; fi ; od ; od ; od ; RETURN(a) ; end: rowmax := 15 : a := A114905(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[Length@ w + 1]]], {0}, 13] // Flatten (* Michael De Vlieger, Sep 06 2017 *)

Crossrefs

Cf. A114906, A114919, A114920.

Sequence in context: A296976 A182321 A285731 * A200651 A126597 A261867

Adjacent sequences: A114902 A114903 A114904 * A114906 A114907 A114908

Keyword

nonn,tabl

Author

Leroy Quet, Jan 06 2006

Extensions

Corrected and extended by R. J. Mathar, Mar 13 2007

Status

approved