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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}.
1
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
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
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved