OFFSET
1,1
COMMENTS
LINKS
John Tyler Rascoe, Table of n, a(n) for n = 1..10000
EXAMPLE
The binary indices of 130 are {2,8}, and the prime indices are {1,3,6}. Both sum to 10, so 130 is in the sequence.
The terms together with their prime indices begin:
19: {8}
33: {2,5}
34: {1,7}
69: {2,9}
74: {1,12}
82: {1,13}
130: {1,3,6}
133: {4,8}
305: {3,18}
412: {1,1,27}
428: {1,1,28}
The terms together with their binary expansions and binary indices begin:
19: 10011 ~ {1,2,5}
33: 100001 ~ {1,6}
34: 100010 ~ {2,6}
69: 1000101 ~ {1,3,7}
74: 1001010 ~ {2,4,7}
82: 1010010 ~ {2,5,7}
130: 10000010 ~ {2,8}
133: 10000101 ~ {1,3,8}
305: 100110001 ~ {1,5,6,9}
412: 110011100 ~ {3,4,5,8,9}
428: 110101100 ~ {3,4,6,8,9}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], Total[prix[#]]==Total[bix[#]]&]
CROSSREFS
For length instead of sum we get A071814.
Positions of zeros in A372428.
For maximum instead of sum we have A372436.
A003963 gives product of prime indices.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
A326031 gives weight of the set-system with BII-number n.
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, May 01 2024
STATUS
approved