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A254539 T(n,k)=Number of length n 1..(k+2) arrays with no leading partial sum equal to a prime.

%I A254539 #6 Jul 23 2025 14:47:03
%S A254539 1,2,1,2,3,1,3,5,8,2,3,10,15,20,4,4,11,40,45,50,6,5,20,49,160,135,126,
%T A254539 11,6,28,105,222,670,421,329,20,6,37,163,576,1087,3001,1466,956,33,7,
%U A254539 41,253,1026,3383,5604,13503,5403,2897,62,7,54,307,1849,6814,20393,29038,60408
%N A254539 T(n,k)=Number of length n 1..(k+2) arrays with no leading partial sum equal to a prime.
%C A254539 Table starts
%C A254539 ..1....2.....2.......3.......3........4........5.........6.........6..........7
%C A254539 ..1....3.....5......10......11.......20.......28........37........41.........54
%C A254539 ..1....8....15......40......49......105......163.......253.......307........466
%C A254539 ..2...20....45.....160.....222......576.....1026......1849......2461.......4195
%C A254539 ..4...50...135.....670....1087.....3383.....6814.....13843.....20012......37643
%C A254539 ..6..126...421....3001....5604....20393....45472....102595....161277.....338402
%C A254539 .11..329..1466...13503...29038...121774...297210....758766...1313695....3093457
%C A254539 .20..956..5403...60408..150268...709169..1936867...5719495..10916298...28507728
%C A254539 .33.2897.19417..270370..764508..4121638.12941917..43758333..91142820..262001403
%C A254539 .62.8341.69205.1192385.3857845.24622476.88456127.333905794.755234611.2410105286
%H A254539 R. H. Hardin, <a href="/A254539/b254539.txt">Table of n, a(n) for n = 1..9999</a>
%e A254539 Some solutions for n=4 k=4
%e A254539 ..4....4....6....6....6....4....4....6....1....4....6....1....4....1....6....6
%e A254539 ..4....6....6....3....2....6....2....6....5....5....6....5....6....3....3....2
%e A254539 ..1....5....4....5....1....2....2....2....2....1....2....6....6....5....1....4
%e A254539 ..1....5....4....2....6....2....1....1....1....2....2....6....4....3....5....4
%Y A254539 Row 1 is A062298(n+2)
%K A254539 nonn,tabl
%O A254539 1,2
%A A254539 _R. H. Hardin_, Feb 01 2015