A370134 - OEIS

A370134

Triangle read by rows: T(n,k) = A002110(n) + A002110(k), 1 <= k <= n; sums of two primorials > 1, not necessarily distinct.

4, 8, 12, 32, 36, 60, 212, 216, 240, 420, 2312, 2316, 2340, 2520, 4620, 30032, 30036, 30060, 30240, 32340, 60060, 510512, 510516, 510540, 510720, 512820, 540540, 1021020, 9699692, 9699696, 9699720, 9699900, 9702000, 9729720, 10210200, 19399380, 223092872, 223092876, 223092900, 223093080, 223095180, 223122900, 223603380

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..5050; the first 100 rows of triangle, flattened

Index entries for sequences related to primorial numbers

FORMULA

For n >= 1, A276150(a(n)) = 2.

EXAMPLE

Triangle begins as:

8, 12;

32, 36, 60;

212, 216, 240, 420;

2312, 2316, 2340, 2520, 4620;

30032, 30036, 30060, 30240, 32340, 60060;

510512, 510516, 510540, 510720, 512820, 540540, 1021020;

9699692, 9699696, 9699720, 9699900, 9702000, 9729720, 10210200, 19399380;

MATHEMATICA

nn = 20; MapIndexed[Set[P[First[#2] - 1], #1] &, FoldList[Times, 1, Prime@ Range[nn + 1]]]; Table[(P[n] + P[k]), {n, nn}, {k, n}] (* Michael De Vlieger, Mar 08 2024 *)

PROG

(PARI)

A002110(n) = prod(i=1, n, prime(i));

A370134(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2); (A002110(1+c) + A002110(1+n - binomial(c + 1, 2))); };

CROSSREFS

A370121 without its leftmost column. Subsequence of A370132.

Cf. A002110, A049345, A087112, A276150, A370135.

Cf. A088860 (right edge).

Sequence in context: A302829 A055079 A081833 * A035403 A050908 A232901

Adjacent sequences: A370131 A370132 A370133 * A370135 A370136 A370137

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Mar 07 2024

STATUS

approved