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

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..5049; the first 100 rows of triangle, flattened

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

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

Adjacent sequences: A370118 A370119 A370120 * A370122 A370123 A370124

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 29 2024

Status

approved