cp's OEIS Frontend

A372471 Irregular triangle read by rows where row n lists the binary indices of the n-th prime number.

%I A372471 #7 May 10 2024 09:27:40
%S A372471 2,1,2,1,3,1,2,3,1,2,4,1,3,4,1,5,1,2,5,1,2,3,5,1,3,4,5,1,2,3,4,5,1,3,
%T A372471 6,1,4,6,1,2,4,6,1,2,3,4,6,1,3,5,6,1,2,4,5,6,1,3,4,5,6,1,2,7,1,2,3,7,
%U A372471 1,4,7,1,2,3,4,7,1,2,5,7,1,4,5,7,1,6,7
%N A372471 Irregular triangle read by rows where row n lists the binary indices of the n-th prime number.
%C A372471 A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
%e A372471 We have prime(12) = (2^1 + 2^3 + 2^6)/2, so row 12 is (1,3,6).
%e A372471 Each prime followed by its binary indices:
%e A372471    2: 2
%e A372471    3: 1 2
%e A372471    5: 1 3
%e A372471    7: 1 2 3
%e A372471   11: 1 2 4
%e A372471   13: 1 3 4
%e A372471   17: 1 5
%e A372471   19: 1 2 5
%e A372471   23: 1 2 3 5
%e A372471   29: 1 3 4 5
%e A372471   31: 1 2 3 4 5
%e A372471   37: 1 3 6
%e A372471   41: 1 4 6
%e A372471   43: 1 2 4 6
%e A372471   47: 1 2 3 4 6
%t A372471 Table[Join@@Position[Reverse[IntegerDigits[Prime[n],2]],1],{n,15}]
%Y A372471 Row lengths are A014499.
%Y A372471 Second column is A023506(n) + 1.
%Y A372471 Final column is A035100.
%Y A372471 Prime-indexed rows of A048793.
%Y A372471 Row-sums are A372429, restriction of A029931 (sum of binary indices).
%Y A372471 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372471 A029837 gives greatest binary index, least A001511.
%Y A372471 A048793 lists binary indices, length A000120, reverse A272020.
%Y A372471 A070939 gives length of binary expansion.
%Y A372471 Cf. A000040, A005940, A056239, A071814, A096111, A191232, A230877, A231204, A372427-A372442.
%K A372471 nonn,tabf,base
%O A372471 1,1
%A A372471 _Gus Wiseman_, May 07 2024