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%I #4 Mar 30 2012 17:34:11
%S 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,
%T 0,0,0,0,2,5,18,70,101,253,409,502,710,1038,1297,1350,1383,1297,1225,
%U 931,710,409,141,70,47,18,10,2
%N 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}.
%C The irregular triangle of numbers is:
%C .
%C .Prime...Prime...........Frequency.with.which.different.prime
%C .Index...................sums.occur
%C ..................N......2..........3..........4..........5
%C .
%C ..1........2.............0..........0..........0..........0
%C ..2........3.............1..........0..........0..........0
%C ..3........5.............2..........0..........0..........0
%C ..4........7.............1..........1..........0..........0
%C ..5.......11........................5..........1..........0
%C ..6.......13........................7..........3..........0
%C ..7.......17........................7.........11..........2
%C ..8.......19........................5.........18..........5
%C ..9.......23........................1.........38.........18
%C .10.......29..................................71.........70
%C .11.......31..................................79........101
%C .12.......37..................................79........253
%C .13.......41..................................61........409
%C .14.......43..................................50........502
%C .15.......47..................................27........710
%C .16.......53...................................6.......1038
%C .17.......59...........................................1297
%C .18.......61...........................................1350
%C .19.......67...........................................1383
%C .20.......71...........................................1297
%C .21.......73...........................................1225
%C .22.......79............................................931
%C .23.......83............................................710
%C .24.......89............................................409
%C .25.......97............................................141
%C .26......101.............................................70
%C .27......103.............................................47
%C .28......107.............................................18
%C .29......109.............................................10
%C .30......113..............................................2
%C .
%C .Totals..................4.........26........444......11998
%e If N = 2 then there are 4 subsets of set {1,2,3,4} with prime sums:
%e .Subset..Sum
%e .{1,2}....3
%e .{1,4}....5
%e .{2,3}....5
%e .{3,4}....7
%e These sums can be represented by:
%e .Prime...Prime...Freq
%e .Index
%e .1.........2.......0
%e .2.........3.......1
%e .3.........5.......2
%e .4.........7.......1
%e The numbers under Freq give the first 4 terms of the sequence.
%Y A167147 = Column sums of the table above.
%K nonn,tabf
%O 1,3
%A _Christopher Hunt Gribble_, Nov 01 2009
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