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 A300789 Heinz numbers of integer partitions whose Young diagram can be tiled by dominos. 6
 1, 3, 4, 7, 9, 10, 12, 13, 16, 19, 21, 22, 25, 27, 28, 29, 34, 36, 37, 39, 40, 43, 46, 48, 49, 52, 53, 55, 57, 61, 62, 63, 64, 70, 71, 75, 76, 79, 81, 82, 84, 85, 87, 88, 89, 90, 91, 94, 100, 101, 107, 108, 111, 112, 113, 115, 116, 117, 118, 121, 129, 130, 131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This sequence is conjectured to be the Heinz numbers of integer partitions in which the odd parts appear as many times in even as in odd positions. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..20000 Solomon W. Golomb, Tiling with polyominoes, Journal of Combinatorial Theory, 1-2 (1966), 280-296. Wikipedia, Domino tiling EXAMPLE Sequence of integer partitions whose Young diagram can be tiled by dominos begins: (), (2), (11), (4), (22), (31), (211), (6), (1111), (8), (42), (51), (33), (222), (411). MAPLE a:= proc(n) option remember; local k; for k from 1+       `if`(n=1, 0, a(n-1)) while (l-> add(`if`(l[i]::odd,        (-1)^i, 0), i=1..nops(l))<>0)(sort(map(i->        numtheory[pi](i[1])\$i[2], ifactors(k)[2]))) do od; k     end: seq(a(n), n=1..100);  # Alois P. Heinz, May 22 2018 MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], Total[(-1)^Flatten[Position[primeMS[#], _?OddQ]]]===0&] (* Conjectured *) CROSSREFS Cf. A000712, A000898, A001405, A004003, A045931, A097613, A099390, A299926, A300056, A300060, A300787, A300788, A304662. Sequence in context: A213508 A088958 A300061 * A026225 A026140 A233010 Adjacent sequences:  A300786 A300787 A300788 * A300790 A300791 A300792 KEYWORD nonn AUTHOR Gus Wiseman, Mar 12 2018 STATUS approved

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Last modified April 2 19:05 EDT 2020. Contains 333190 sequences. (Running on oeis4.)