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A382879 Positions of 0 in A382857 (permutations of prime indices with equal run-lengths).

%I A382879 #8 Apr 21 2025 10:47:08
%S A382879 24,40,48,54,56,80,88,96,104,112,135,136,152,160,162,176,184,189,192,
%T A382879 208,224,232,240,248,250,272,288,296,297,304,320,328,336,344,351,352,
%U A382879 368,375,376,384,405,416,424,448,459,464,472,480,486,488,496,513,528,536
%N A382879 Positions of 0 in A382857 (permutations of prime indices with equal run-lengths).
%C A382879 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798, sum A056239.
%e A382879 The terms together with their prime indices begin:
%e A382879    24: {1,1,1,2}
%e A382879    40: {1,1,1,3}
%e A382879    48: {1,1,1,1,2}
%e A382879    54: {1,2,2,2}
%e A382879    56: {1,1,1,4}
%e A382879    80: {1,1,1,1,3}
%e A382879    88: {1,1,1,5}
%e A382879    96: {1,1,1,1,1,2}
%e A382879   104: {1,1,1,6}
%e A382879   112: {1,1,1,1,4}
%e A382879   135: {2,2,2,3}
%e A382879   136: {1,1,1,7}
%e A382879   152: {1,1,1,8}
%e A382879   160: {1,1,1,1,1,3}
%t A382879 Select[Range[100], Select[Permutations[Join@@ConstantArray@@@FactorInteger[#]], SameQ@@Length/@Split[#]&]=={}&]
%Y A382879 For distinct instead of equal the complement is A351294, counted by A239455.
%Y A382879 For distinct instead of equal we have A351295, counted by A351293.
%Y A382879 For run-sums instead of run-lengths we have A383100, zeros of A382877, distinct A382876.
%Y A382879 Positions of 0 in A382857 (firsts A382878), by signature A382858 (distinct A382773).
%Y A382879 For prime signature instead of prime indices we have A382914.
%Y A382879 Partitions of this type are counted by A382915.
%Y A382879 The complement is counted by A383013.
%Y A382879 A005811 counts runs in binary expansion.
%Y A382879 A056239 adds up prime indices, row sums of A112798.
%Y A382879 A297770 counts distinct runs in binary expansion.
%Y A382879 A164707 lists numbers whose binary form has equal runs of ones, distinct A328592.
%Y A382879 A304442 counts partitions with equal run-sums, ranks A353833.
%Y A382879 A329739 counts compositions with distinct run-lengths, ranks A351290.
%Y A382879 A353744 ranks compositions with equal run-lengths, distinct A351596 (complement A351291).
%Y A382879 Cf. A000720, A000961, A001221, A001222, A003242, A008480, A047966, A130091, A238279, A351201.
%K A382879 nonn
%O A382879 1,1
%A A382879 _Gus Wiseman_, Apr 09 2025