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A138152 Triangular sequence: a(n, m) = a(n - 1, m) + 10 and a(n,m) + 2*ceiling(log(1+k)), k <= n.

%I A138152 #10 Jun 03 2023 06:18:14
%S A138152 3,7,11,13,17,19,23,29,31,31,37,41,41,43,47,53,59,61,61,67,71,71,73,
%T A138152 79,83,83,89,97,101,103,101,103,107,109,113,113,127,131,131,137,139,
%U A138152 149,151,151,157,163,163,167,173,173,179,181,181,191,193,197,199
%N A138152 Triangular sequence: a(n, m) = a(n - 1, m) + 10 and a(n,m) + 2*ceiling(log(1+k)), k <= n.
%C A138152 Row sums: {10, 60, 83, 109, 131, 173, 199, 306, 172, 301, 533, 113, 258, 407, 300, 471, 503, 533, 181, 780, ...}.
%C A138152 The procedure is based on the modulo-10 prime ending set {1,3,7,9} and leaves out {2,5} at the start. To n=20 the precedure produces all the primes except {2,5}. It also classifies primes by the length of the longest vector in which they appear.
%F A138152 a(0, m) = {0,1,3,7,9};
%F A138152 a(n, m) = a(n-1, m) + 10;
%F A138152 a(n, m) = If( prime,{a(n,m),a(n,m)+2*ceiling(log(1+k)),k <= n).
%e A138152 Rows begin
%e A138152     3,   7;
%e A138152    11,  13,  17,  19;
%e A138152    23,  29,  31;
%e A138152    31,  37,  41;
%e A138152    41,  43,  47;
%e A138152    53,  59,  61;
%e A138152    61,  67,  71;
%e A138152    71,  73,  79,  83;
%e A138152    83,  89;
%e A138152    97, 101, 103;
%e A138152   101, 103, 107, 109, 113;
%e A138152   113;
%e A138152   127, 131;
%e A138152   131, 137, 139;
%e A138152   149, 151;
%e A138152   151, 157, 163;
%e A138152   163, 167, 173;
%e A138152   173, 179, 181;
%e A138152   181;
%e A138152   191, 193, 197, 199;
%t A138152 a[0, 0] = 0; a[0, 1] = 1; a[0, 2] = 3; a[0, 3] = 7; a[0, 4] = 9; a[n_, m_] := a[n, m] = a[n - 1, m] + 10; a0 = Table[Union[Flatten[Table[If[PrimeQ[a[n, m]] && PrimeQ[a[n, m] + 2*k], {a[n, m], a[n, m] + 2*k}, {}], {m, 0, 4}, {k, 0, Ceiling[Log[1 +n]]}]]], {n, 0, 20}]; Flatten[a0]
%K A138152 nonn,tabf,uned
%O A138152 1,1
%A A138152 _Roger L. Bagula_, May 04 2008