cp's OEIS Frontend

A372516 Number of ones minus number of zeros in the binary expansion of the n-th prime number.

%I A372516 #8 May 09 2025 16:00:31
%S A372516 0,2,1,3,2,2,-1,1,3,3,5,0,0,2,4,2,4,4,-1,1,-1,3,1,1,-1,1,3,3,3,1,7,-2,
%T A372516 -2,0,0,2,2,0,2,2,2,2,6,-2,0,2,2,6,2,2,2,6,2,6,-5,-1,-1,1,-1,-1,1,-1,
%U A372516 1,3,1,3,1,-1,3,3,-1,3,5,3,5,7,-1,1,-1,1,1
%N A372516 Number of ones minus number of zeros in the binary expansion of the n-th prime number.
%C A372516 Absolute value is A177718.
%F A372516 a(n) = A000120(A000040(n)) - A080791(A000040(n)).
%F A372516 a(n) = A014499(n) - A035103(n).
%F A372516 a(n) = A145037(A000040(n))
%e A372516 The binary expansion of 83 is (1,0,1,0,0,1,1), and 83 is the 23rd prime, so a(23) = 4 - 3 = 1.
%t A372516 Table[DigitCount[Prime[n],2,1]-DigitCount[Prime[n],2,0],{n,100}]
%t A372516 DigitCount[#,2,1]-DigitCount[#,2,0]&/@Prime[Range[100]] (* _Harvey P. Dale_, May 09 2025 *)
%Y A372516 The sum instead of difference is A035100, firsts A372684 (primes A104080).
%Y A372516 The negative version is A037861(A000040(n)).
%Y A372516 Restriction of A145037 to the primes.
%Y A372516 The unsigned version is A177718.
%Y A372516 - Positions of zeros are A177796, indices of the primes A066196.
%Y A372516 - Positions of positive terms are indices of the primes A095070.
%Y A372516 - Positions of negative terms are indices of the primes A095071.
%Y A372516 - Positions of negative ones are A372539, indices of the primes A095072.
%Y A372516 - Positions of ones are A372538, indices of the primes A095073.
%Y A372516 - Positions of nonnegative terms are indices of the primes A095074.
%Y A372516 - Positions of nonpositive terms are indices of the primes A095075.
%Y A372516 A000120 counts ones in binary expansion (binary weight), zeros A080791.
%Y A372516 A030190 gives binary expansion, reversed A030308.
%Y A372516 A035103 counts zeros in binary expansion of primes, firsts A372474.
%Y A372516 A048793 lists binary indices, reverse A272020, sum A029931.
%Y A372516 A070939 gives length of binary expansion.
%Y A372516 A101211 lists run-lengths in binary expansion, row-lengths A069010.
%Y A372516 A372471 lists the binary indices of each prime.
%Y A372516 Cf. A000043, A003714, A005940, A059305, A061712, A066195, A071814, A211997, A372429, A372517, A372686.
%K A372516 sign
%O A372516 1,2
%A A372516 _Gus Wiseman_, May 13 2024