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A114906
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Triangle where a(1,1) = 1; a(n,m) = number of terms in row (n-1) which, when added to m, are primes.
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4
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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
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OFFSET
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1,4
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COMMENTS
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LINKS
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EXAMPLE
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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].
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MAPLE
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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
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MATHEMATICA
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NestList[Function[w, Map[Function[k, Count[Map[k + # &, w], _?PrimeQ]], Range[Length@ w + 1]]], {1}, 13] // Flatten (* Michael De Vlieger, Sep 06 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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