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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.
7
2, 3, 4, 7, 8, 12, 31, 32, 36, 60, 211, 212, 216, 240, 420, 2311, 2312, 2316, 2340, 2520, 4620, 30031, 30032, 30036, 30060, 30240, 32340, 60060, 510511, 510512, 510516, 510540, 510720, 512820, 540540, 1021020, 9699691, 9699692, 9699696, 9699720, 9699900, 9702000, 9729720, 10210200, 19399380, 223092871, 223092872
OFFSET
0,1
COMMENTS
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.
FORMULA
For n >= 1, A276150(a(n)) = 2.
For n >= 1, A276086(a(n)) = A087112(1+n).
EXAMPLE
Triangle begins as:
2;
3, 4;
7, 8, 12;
31, 32, 36, 60;
211, 212, 216, 240, 420;
2311, 2312, 2316, 2340, 2520, 4620;
30031, 30032, 30036, 30060, 30240, 32340, 60060;
510511, 510512, 510516, 510540, 510720, 512820, 540540, 1021020;
9699691, 9699692, 9699696, 9699720, 9699900, 9702000, 9729720, 10210200, 19399380;
PROG
(PARI)
A002110(n) = prod(i=1, n, prime(i));
A370121(n) = { my(c = (sqrtint(8*n + 1) - 1) \ 2); (A002110(c) + A002110(n - binomial(c + 1, 2))); };
CROSSREFS
Cf. A002110, A049345, A087112, A276086, A276150, A370129 (arithmetic derivative applied to this triangle).
Cf. A006862 (left edge), A088860 (right edge).
Cf. A177689 (same triangle without the right edge), A370134 (without the leftmost column).
Subsequence of A370132.
Cf. also A173786.
Sequence in context: A301806 A374057 A066847 * A057887 A202116 A215914
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Feb 29 2024
STATUS
approved