A114906 Triangle where a(1,1) = 1; a(n,m) = number of terms in row (n-1) which, when added to m, are primes.

1, 1, 1, 2, 2, 0, 2, 1, 3, 0, 2, 3, 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

1,4

Comments

Rows n >= 6 are identical to those in A114905. - R. J. Mathar, Mar 13 2007

Links

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

Example

Row 4 of the triangle is [2,1,3,0]. Adding 1 to these gives [3,2,4,1], of which 2 terms are primes. Adding 2 to these gives [4,3,5,2], of which 3 terms are primes. Adding 3 to these gives [5,4,6,3], of which 2 terms are primes. Adding 4 to these gives [6,5,7,4], of which 2 terms are primes. And adding 5 to these gives [7,6,8,5], of which 2 terms are primes. So row 5 is [2,3,2,2,2].

Maple

A114906 := proc(rowmax) local a, n, m, t ; a := matrix(rowmax, rowmax) ; a[1, 1] := 1 ; 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 := A114906(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]]], {1}, 13] // Flatten (* Michael De Vlieger, Sep 06 2017 *)

Crossrefs

Cf. A114905, A114919, A114920.

Sequence in context: A352362 A236374 A045719 * A259179 A214667 A214665

Adjacent sequences: A114903 A114904 A114905 * A114907 A114908 A114909

Keyword

nonn,tabl

Author

Leroy Quet, Jan 06 2006

Extensions

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

Status

approved