cp's OEIS Frontend

A372429 Sum of binary indices of prime(n). Sum of positions of ones in the reversed binary expansion of prime(n).

%I A372429 #16 May 22 2024 02:12:25
%S A372429 2,3,4,6,7,8,6,8,11,13,15,10,11,13,16,15,18,19,10,13,12,17,15,17,14,
%T A372429 17,19,20,21,19,28,11,13,15,17,19,21,17,20,22,22,23,29,16,19,21,23,30,
%U A372429 24,25,26,31,27,33,10,15,17,19,18,19,21,19,23,26,25,28,23
%N A372429 Sum of binary indices of prime(n). Sum of positions of ones in the reversed binary expansion of prime(n).
%C A372429 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.
%C A372429 Do 2, 3, 4, 7, 12, 14 appear just once?
%C A372429 Are 1, 5, 9 missing?
%C A372429 The above questions hold true up to n = 10^6. - _John Tyler Rascoe_, May 21 2024
%H A372429 John Tyler Rascoe, <a href="/A372429/b372429.txt">Table of n, a(n) for n = 1..9438</a>
%F A372429 a(n) = A029931(prime(n)).
%e A372429 The primes together with their binary expansions and binary indices begin:
%e A372429    2:      10 ~ {2}
%e A372429    3:      11 ~ {1,2}
%e A372429    5:     101 ~ {1,3}
%e A372429    7:     111 ~ {1,2,3}
%e A372429   11:    1011 ~ {1,2,4}
%e A372429   13:    1101 ~ {1,3,4}
%e A372429   17:   10001 ~ {1,5}
%e A372429   19:   10011 ~ {1,2,5}
%e A372429   23:   10111 ~ {1,2,3,5}
%e A372429   29:   11101 ~ {1,3,4,5}
%e A372429   31:   11111 ~ {1,2,3,4,5}
%e A372429   37:  100101 ~ {1,3,6}
%e A372429   41:  101001 ~ {1,4,6}
%e A372429   43:  101011 ~ {1,2,4,6}
%e A372429   47:  101111 ~ {1,2,3,4,6}
%e A372429   53:  110101 ~ {1,3,5,6}
%e A372429   59:  111011 ~ {1,2,4,5,6}
%e A372429   61:  111101 ~ {1,3,4,5,6}
%e A372429   67: 1000011 ~ {1,2,7}
%e A372429   71: 1000111 ~ {1,2,3,7}
%e A372429   73: 1001001 ~ {1,4,7}
%e A372429   79: 1001111 ~ {1,2,3,4,7}
%t A372429 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A372429 Table[Total[bix[Prime[n]]],{n,100}]
%Y A372429 The number instead of sum of binary indices is A014499.
%Y A372429 Restriction of A029931 (sum of binary indices) to the primes A000040.
%Y A372429 The maximum instead of sum of binary indices is A035100, see also A023506.
%Y A372429 Row-sums of A372471.
%Y A372429 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372429 A029837 gives greatest binary index, least A001511.
%Y A372429 A048793 lists binary indices, length A000120, reverse A272020.
%Y A372429 A056239 adds up prime indices.
%Y A372429 A070939 gives length of binary expansion.
%Y A372429 A096111 gives product of binary indices.
%Y A372429 A326031 gives weight of the set-system with BII-number n.
%Y A372429 A372427 lists numbers whose binary and prime indices have the same sum.
%Y A372429 Cf. A005940, A030101, A059893, A071814, A230877, A231204, A358134, A359359, A359401, A372430-A372437, A372441.
%K A372429 nonn,base
%O A372429 1,1
%A A372429 _Gus Wiseman_, May 02 2024