A167365 Irregular triangle read by columns: Frequency with which different primes result from the sum of the members of each subset of size N of the set {1..N^2}.

0, 1, 2, 1, 0, 0, 0, 1, 5, 7, 7, 5, 1, 0, 0, 0, 0, 1, 3, 11, 18, 38, 71, 79, 79, 61, 50, 27, 6, 0, 0, 0, 0, 0, 2, 5, 18, 70, 101, 253, 409, 502, 710, 1038, 1297, 1350, 1383, 1297, 1225, 931, 710, 409, 141, 70, 47, 18, 10, 2

Offset

1,3

Comments

The irregular triangle of numbers is:

.

.Prime...Prime...........Frequency.with.which.different.prime

.Index...................sums.occur

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

.

..1........2.............0..........0..........0..........0

..2........3.............1..........0..........0..........0

..3........5.............2..........0..........0..........0

..4........7.............1..........1..........0..........0

..5.......11........................5..........1..........0

..6.......13........................7..........3..........0

..7.......17........................7.........11..........2

..8.......19........................5.........18..........5

..9.......23........................1.........38.........18

.10.......29..................................71.........70

.11.......31..................................79........101

.12.......37..................................79........253

.13.......41..................................61........409

.14.......43..................................50........502

.15.......47..................................27........710

.16.......53...................................6.......1038

.17.......59...........................................1297

.18.......61...........................................1350

.19.......67...........................................1383

.20.......71...........................................1297

.21.......73...........................................1225

.22.......79............................................931

.23.......83............................................710

.24.......89............................................409

.25.......97............................................141

.26......101.............................................70

.27......103.............................................47

.28......107.............................................18

.29......109.............................................10

.30......113..............................................2

.

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

Links

Table of n, a(n) for n=1..58.

Example

If N = 2 then there are 4 subsets of set {1,2,3,4} with prime sums:
.Subset..Sum
.{1,2}....3
.{1,4}....5
.{2,3}....5
.{3,4}....7
These sums can be represented by:
.Prime...Prime...Freq
.Index
.1.........2.......0
.2.........3.......1
.3.........5.......2
.4.........7.......1
The numbers under Freq give the first 4 terms of the sequence.

Crossrefs

A167147 = Column sums of the table above.

Sequence in context: A091006 A350433 A373480 * A211996 A359326 A352245

Adjacent sequences: A167362 A167363 A167364 * A167366 A167367 A167368

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Nov 01 2009

Status

approved