A132403 Analog of Pascal's triangle, but with "next prime" applied to each sum.

1, 2, 2, 3, 5, 3, 5, 11, 11, 5, 7, 17, 23, 17, 7, 11, 29, 41, 41, 29, 11, 13, 41, 71, 83, 71, 41, 13, 17, 59, 113, 157, 157, 113, 59, 17, 19, 79, 173, 271, 317, 271, 173, 79, 19, 23, 101, 257, 449, 593, 593, 449, 257, 101, 23, 29, 127, 359, 709, 1049, 1187, 1049, 709, 359

Offset

0,2

Comments

Each number is the smallest prime => the sum of the 2 numbers above (consider each line padded with 0 on each side).

Links

Table of n, a(n) for n=0..63.

Formula

Array read by rows: A[k+1,n] = nextprime(A[k,n] + A[k,n+1]) = A007918(A[k,n] + A[k,n+1]).

Example

Triangle begins:
1
2....2
3....5....3
5...11...11....5
7...17...23...17....7
11..29...41...41...29...11
13..41...71...83...71...41...13
17..59..113..157..157..113...59...17
19..79..173..271..317..271..173...79...19
23.101..257..449..593..593..449..257..101...23
29.127..359..709.1049.1187.1049..709..359..127..29
31.157..487.1069.1759.2237.2237.1759.1069..487.157..31
37.191..647.1559.2833.4001.4583.4001.2833.1559.647.191.37.
First column is primes A000040. Second column is A064337. Analog of central binomial coefficient A000984 is the central numbers in this triangle, beginning: 1, 5, 23, 83, 317, 1187, 4583, 17327. Different triangles result if the first row is a pair other than (2,2). Asymmetric triangles occur if the first row consists of unequal integers.
The number under the middle of the row (2, 2) is 5 because 5 is smallest prime equal to or greater than 2+2 = 4.

Crossrefs

Cf. A000040, A000984, A007918, A007308, A064337.

Sequence in context: A317160 A317043 A317697 * A209167 A299995 A113167

Adjacent sequences: A132400 A132401 A132402 * A132404 A132405 A132406

Keyword

easy,nonn,tabl

Author

Jonathan Vos Post, Nov 12 2007

Status

approved