

A131424


Triangle read by rows: T(n,k) = prime(n) + prime(k)  3, 1 <= k <= n.


3



1, 2, 3, 4, 5, 7, 6, 7, 9, 11, 10, 11, 13, 15, 19, 12, 13, 15, 17, 21, 23, 16, 17, 19, 21, 25, 27, 31, 18, 19, 21, 23, 27, 29, 33, 35, 22, 23, 25, 27, 31, 33, 37, 39, 43, 28, 29, 31, 33, 37, 39, 43, 45, 49, 55, 30, 31, 33, 35, 39, 41, 45, 47, 51, 57, 59
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OFFSET

1,2


COMMENTS

Left border = A006093, (primes  1): (1, 2, 4, 6, 10, 12, ...). Right border = A131426 (2*primes  3): (1, 3, 7, 11, 19, 23, 31, ...). Row sums = A131425: (1, 5, 16, 33, 68, 101, 156, ...).


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)


FORMULA

Equals (A000012 * A127640) + (A127640 * A000012)  3*A000012 as infinite lower triangular matrices.


EXAMPLE

First few rows of the triangle are:
1;
2, 3;
4, 5, 7;
6, 7, 9, 11;
10, 11, 13, 15, 19;
12, 13, 15, 17, 21, 23;
16, 17, 19, 21, 25, 27, 31;
18, 19, 21, 23, 27, 29, 33, 35;
22, 23, 25, 27, 31, 33, 37, 39, 43;
...


PROG

(PARI) T(n, k) = if(k<=n, prime(n) + prime(k)  3, 0) \\ Andrew Howroyd, Sep 01 2018


CROSSREFS

Row sums are A131425.
Cf. A127640, A131426, A006093, A000040.
Sequence in context: A085729 A331269 A073907 * A336285 A222249 A230565
Adjacent sequences: A131421 A131422 A131423 * A131425 A131426 A131427


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Jul 10 2007


EXTENSIONS

Name clarified and terms a(56) and beyond from Andrew Howroyd, Sep 01 2018


STATUS

approved



