A167400 Irregular triangle read by columns: frequency with which the value of the first subset member occurs in each subset of size N of the set {1..N^2}, whose members sum to a prime number.

2, 1, 1, 8, 8, 4, 4, 1, 1, 111, 88, 67, 55, 42, 32, 23, 15, 6, 3, 2, 2470, 2022, 1688, 1358, 1119, 880, 702, 520, 393, 268, 189, 122, 87, 57, 48, 33, 24, 11, 6, 1

Offset

2,1

Comments

The sequence is related to the method of subset construction, in which

the far left-hand member increases most slowly in value.

The.irregular.triangle.of.numbers.is:

First...........Frequency.with.which.the.value.of

Member..........the.first.subset.member.occurs

..........N.....2..........3..........4..........5

.

.1..............2..........8........111.......2470

.2..............1..........8.........88.......2022

.3..............1..........4.........67.......1688

.4.........................4.........55.......1358

.5.........................1.........42.......1119

.6.........................1.........32........880

.7...................................23........702

.8...................................15........520

.9....................................6........393

10....................................3........268

11....................................2........189

12.............................................122

13..............................................87

14..............................................57

15..............................................48

16..............................................33

17..............................................24

18..............................................11

19...............................................6

20...............................................1

.

.Totals.........4.........26........444......11998

Links

Table of n, a(n) for n=2..41.

Example

For N = 2, the subsets of {1, 2, 3, 4} whose members sum to primes are
{1, 2}, {1, 4}, {2, 3}, {3, 4}
The first member is 1 in 2 subsets, 2 in 1 subset and 3 in 1 subset,
giving the first 3 terms of the sequence: 2, 1, 1.

Crossrefs

A167147 = Column sums of the table above.

Sequence in context: A176698 A129276 A156901 * A225848 A165889 A087127

Adjacent sequences: A167397 A167398 A167399 * A167401 A167402 A167403

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Nov 02 2009

Status

approved