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

24, 40, 48, 54, 56, 80, 88, 96, 104, 112, 135, 136, 152, 160, 162, 176, 184, 189, 192, 208, 224, 232, 240, 248, 250, 272, 288, 296, 297, 304, 320, 328, 336, 344, 351, 352, 368, 375, 376, 384, 405, 416, 424, 448, 459, 464, 472, 480, 486, 488, 496, 513, 528, 536

Offset: 1

Author

Gus Wiseman, Apr 09 2025

Keywords

• nonn

Comments

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.

Examples

			The terms together with their prime indices begin:
   24: {1,1,1,2}
   40: {1,1,1,3}
   48: {1,1,1,1,2}
   54: {1,2,2,2}
   56: {1,1,1,4}
   80: {1,1,1,1,3}
   88: {1,1,1,5}
   96: {1,1,1,1,1,2}
  104: {1,1,1,6}
  112: {1,1,1,1,4}
  135: {2,2,2,3}
  136: {1,1,1,7}
  152: {1,1,1,8}
  160: {1,1,1,1,1,3}
		

Crossrefs

For distinct instead of equal the complement is A351294, counted by A239455.

For distinct instead of equal we have A351295, counted by A351293.

For run-sums instead of run-lengths we have A383100, zeros of A382877, distinct A382876.

Positions of 0 in A382857 (firsts A382878), by signature A382858 (distinct A382773).

For prime signature instead of prime indices we have A382914.

Partitions of this type are counted by A382915.

The complement is counted by A383013.

A005811 counts runs in binary expansion.

A056239 adds up prime indices, row sums of A112798.

A297770 counts distinct runs in binary expansion.

A164707 lists numbers whose binary form has equal runs of ones, distinct A328592.

A304442 counts partitions with equal run-sums, ranks A353833.

A329739 counts compositions with distinct run-lengths, ranks A351290.

A353744 ranks compositions with equal run-lengths, distinct A351596 (complement A351291).

Cf. A000720, A000961, A001221, A001222, A003242, A008480, A047966, A130091, A238279, A351201.

Programs

Mathematica

Select[Range[100], Select[Permutations[Join@@ConstantArray@@@FactorInteger[#]], SameQ@@Length/@Split[#]&]=={}&]