

A114919


Triangle where a(0,0) = 0; a(n,m) = number of terms in row (n1) which, when added to m, are primes.


4



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
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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 n1 do if isprime( m1+a[n1, 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



