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%I #15 Sep 07 2017 09:13:47
%S 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,
%T 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,
%U 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
%N Triangle where a(0,0) = 0; a(n,m) = number of terms in row (n-1) which, when added to m, are primes.
%H Michael De Vlieger, <a href="/A114919/b114919.txt">Table of n, a(n) for n = 0..11627</a> (rows 0 <= n <= 150).
%e 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].
%p 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
%t NestList[Function[w, Map[Function[k, Count[Map[k + # &, w], _?PrimeQ]], Range[0, Length@ w]]], {0}, 13] // Flatten (* _Michael De Vlieger_, Sep 06 2017 *)
%Y Cf. A114920, A114905, A114906.
%K nonn,tabl
%O 0,6
%A _Leroy Quet_, Jan 07 2006
%E More terms from _R. J. Mathar_, Mar 13 2007
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