cp's OEIS Frontend

A353931 Least run-sum of the prime indices of n.

%I A353931 #6 Jun 11 2022 07:55:00
%S A353931 0,1,2,2,3,1,4,3,4,1,5,2,6,1,2,4,7,1,8,2,2,1,9,2,6,1,6,2,10,1,11,5,2,
%T A353931 1,3,2,12,1,2,3,13,1,14,2,3,1,15,2,8,1,2,2,16,1,3,3,2,1,17,2,18,1,4,6,
%U A353931 3,1,19,2,2,1,20,3,21,1,2,2,4,1,22,3,8,1
%N A353931 Least run-sum of the prime indices of n.
%C A353931 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.
%C A353931 Every sequence can be uniquely split into a sequence of non-overlapping runs. For example, the runs of (2,2,1,1,1,3,2,2) are ((2,2),(1,1,1),(3),(2,2)), with sums (4,3,3,4).
%e A353931 The prime indices of 72 are {1,1,1,2,2}, with run-sums {3,4}, so a(72) = 3.
%t A353931 Table[Min@@Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k],{n,100}]
%Y A353931 Positions of first appearances are A008578.
%Y A353931 For run-lengths instead of run-sums we have A051904, greatest A051903.
%Y A353931 For run-sums and binary expansion we have A144790, greatest A038374.
%Y A353931 For run-lengths and binary expansion we have A175597, greatest A043276.
%Y A353931 Distinct run-sums are counted by A353835, weak A353861.
%Y A353931 The greatest run-sum is given by A353862.
%Y A353931 A001222 counts prime factors, distinct A001221.
%Y A353931 A005811 counts runs in binary expansion.
%Y A353931 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A353931 A124010 gives prime signature, sorted A118914.
%Y A353931 A304442 counts partitions with all equal run-sums, compositions A353851.
%Y A353931 A353832 represents the operation of taking run-sums of a partition.
%Y A353931 A353833 ranks partitions with all equal run sums, nonprime A353834.
%Y A353931 A353838 ranks partitions with all distinct run-sums, counted by A353837.
%Y A353931 A353840-A353846 pertain to partition run-sum trajectory.
%Y A353931 Cf. A067340, A073093, A181819, A300273, A316413, A353839, A353866.
%K A353931 nonn
%O A353931 1,3
%A A353931 _Gus Wiseman_, Jun 07 2022