cp's OEIS Frontend

A359754 Positions of first appearances in the sequence of weighted sums of reversed prime indices (A318283).

%I A359754 #6 Jan 16 2023 11:14:59
%S A359754 1,2,3,4,6,8,10,12,16,18,19,24,27,32,36,43,48,59,61,64,67,71,79,83,89,
%T A359754 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,
%U A359754 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269
%N A359754 Positions of first appearances in the sequence of weighted sums of reversed prime indices (A318283).
%C A359754 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 A359754 The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.
%e A359754 The terms together with their prime indices begin:
%e A359754     1: {}
%e A359754     2: {1}
%e A359754     3: {2}
%e A359754     4: {1,1}
%e A359754     6: {1,2}
%e A359754     8: {1,1,1}
%e A359754    10: {1,3}
%e A359754    12: {1,1,2}
%e A359754    16: {1,1,1,1}
%e A359754    18: {1,2,2}
%e A359754    19: {8}
%e A359754    24: {1,1,1,2}
%e A359754    27: {2,2,2}
%e A359754    32: {1,1,1,1,1}
%e A359754    36: {1,1,2,2}
%e A359754    43: {14}
%e A359754    48: {1,1,1,1,2}
%t A359754 nn=100;
%t A359754 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A359754 ots[y_]:=Sum[i*y[[i]],{i,Length[y]}];
%t A359754 seq=Table[ots[Reverse[primeMS[n]]],{n,1,nn}];
%t A359754 Select[Range[nn],FreeQ[seq[[Range[#-1]]],seq[[#]]]&]
%Y A359754 Positions of first appearances in A318283, unreversed A304818.
%Y A359754 This is the sorted version of A359679.
%Y A359754 The zero-based version is A359680, unreversed A359675.
%Y A359754 The unreversed version is A359755, unsorted A359682.
%Y A359754 A053632 counts compositions by weighted sum.
%Y A359754 A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
%Y A359754 A320387 counts multisets by weighted sum, zero-based A359678.
%Y A359754 A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
%Y A359754 Cf. A029931, A089633, A124757, A243055, A358194, A359497, A359674, A359677, A359681, A359683.
%K A359754 nonn
%O A359754 1,2
%A A359754 _Gus Wiseman_, Jan 15 2023