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%I #26 Nov 30 2019 17:25:37
%S 1,2,3,4,5,6,7,8,10,11,12,13,14,16,17,19,20,22,23,24,25,26,27,28,29,
%T 31,32,33,34,36,37,38,39,40,41,43,44,46,47,48,49,51,52,53,54,56,57,58,
%U 59,61,62,64,66,67,68,69,71,72,73,74,76,78,79,80,82,83,85,86,87,88,89,92,93,94,95,96,97,98,100
%N Numbers without repeated parts in their partitions into consecutive parts.
%C All primes are terms. - _Ivan N. Ianakiev_, Nov 05 2019
%C All powers of 2 are terms. - _Omar E. Pol_, Nov 19 2019
%e The partitions of 9 into consecutive parts are [9], [5, 4], [4, 3, 2]. The 4 is a repeated part, so 9 is not in the sequence.
%e The partitions of 10 into consecutive parts are [10], [4, 3, 2, 1]. There are no repeated parts, so 10 is in the sequence.
%t Array[If[Or[PrimeQ@ #, IntegerQ@ Log2@ #], #, # Boole[Count[Tally@ Flatten@ Select[IntegerPartitions[#], Union@ Differences@ # == {-1} &], _?(Last@ # > 1 &)] == 0]] /. 0 -> Nothing &, 60] (* _Michael De Vlieger_, Nov 22 2019 *)
%Y Cf. A001227, A118236 (complement), A286000, A286001, A299765, A328365.
%K nonn
%O 1,2
%A _Omar E. Pol_, Nov 04 2019