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A370121 Triangle read by rows: T(n,k) = A002110(n) + A002110(k), 0 <= k <= n; sums of two primorials, not necessarily distinct.

%I A370121 #15 Mar 08 2024 16:10:48
%S A370121 2,3,4,7,8,12,31,32,36,60,211,212,216,240,420,2311,2312,2316,2340,
%T A370121 2520,4620,30031,30032,30036,30060,30240,32340,60060,510511,510512,
%U A370121 510516,510540,510720,512820,540540,1021020,9699691,9699692,9699696,9699720,9699900,9702000,9729720,10210200,19399380,223092871,223092872
%N A370121 Triangle read by rows: T(n,k) = A002110(n) + A002110(k), 0 <= k <= n; sums of two primorials, not necessarily distinct.
%C A370121 After the initial 2, numbers with either one 2 or two 1's in their primorial base representation (A049345), with all the other digits zeros.
%H A370121 Antti Karttunen, <a href="/A370121/b370121.txt">Table of n, a(n) for n = 0..5049; the first 100 rows of triangle, flattened</a>
%H A370121 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A370121 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A370121 For n >= 1, A276150(a(n)) = 2.
%F A370121 For n >= 1, A276086(a(n)) = A087112(1+n).
%e A370121 Triangle begins as:
%e A370121         2;
%e A370121         3,       4;
%e A370121         7,       8,      12;
%e A370121        31,      32,      36,      60;
%e A370121       211,     212,     216,     240,     420;
%e A370121      2311,    2312,    2316,    2340,    2520,    4620;
%e A370121     30031,   30032,   30036,   30060,   30240,   32340,   60060;
%e A370121    510511,  510512,  510516,  510540,  510720,  512820,  540540,  1021020;
%e A370121   9699691, 9699692, 9699696, 9699720, 9699900, 9702000, 9729720, 10210200, 19399380;
%o A370121 (PARI)
%o A370121 A002110(n) = prod(i=1,n,prime(i));
%o A370121 A370121(n) = { my(c = (sqrtint(8*n + 1) - 1) \ 2); (A002110(c) + A002110(n - binomial(c + 1, 2))); };
%Y A370121 Cf. A002110, A049345, A087112, A276086, A276150, A370129 (arithmetic derivative applied to this triangle).
%Y A370121 Cf. A006862 (left edge), A088860 (right edge).
%Y A370121 Cf. A177689 (same triangle without the right edge), A370134 (without the leftmost column).
%Y A370121 Subsequence of A370132.
%Y A370121 Cf. also A173786.
%K A370121 nonn,tabl
%O A370121 0,1
%A A370121 _Antti Karttunen_, Feb 29 2024