cp's OEIS Frontend

A372686 Sorted list of positions of first appearances in A014499 (number of ones in binary expansion of each prime).

%I A372686 #11 May 15 2024 06:57:40
%S A372686 1,2,4,9,11,31,64,76,167,309,502,801,1028,6363,7281,12079,12251,43237,
%T A372686 43390,146605,291640,951351,1046198,2063216,3957778,11134645,14198321,
%U A372686 28186247,54387475,105097565,249939829,393248783,751545789,1391572698,2182112798,8242984130
%N A372686 Sorted list of positions of first appearances in A014499 (number of ones in binary expansion of each prime).
%C A372686 The unsorted version is A372517.
%H A372686 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamming_weight">Hamming weight</a>.
%F A372686 prime(a(n)) = A372685(n).
%e A372686 The sequence contains 9 because the first 9 terms of A014499 are 1, 2, 2, 3, 3, 3, 2, 3, 4, and the last of these is the first position of 4.
%t A372686 First/@GatherBy[Range[1000],DigitCount[Prime[#],2,1]&]
%Y A372686 Positions of first appearances in A014499.
%Y A372686 The unsorted version is A372517.
%Y A372686 For binary length we have A372684, primes A104080, firsts of A035100.
%Y A372686 Taking primes gives A372685, unsorted version A061712.
%Y A372686 A000120 counts ones in binary expansion (binary weight), zeros A080791.
%Y A372686 A029837 gives greatest binary index, least A001511.
%Y A372686 A030190 gives binary expansion, reversed A030308.
%Y A372686 A035103 counts zeros in binary expansion of each prime, firsts A372474.
%Y A372686 A048793 lists binary indices, reverse A272020, sum A029931.
%Y A372686 A070939 gives length of binary expansion (number of bits).
%Y A372686 A372471 lists binary indices of primes.
%Y A372686 Cf. A000040, A005940, A059015, A066195, A069010, A071814, A211997, A372429, A372433, A372473, A372516.
%K A372686 nonn,base
%O A372686 1,2
%A A372686 _Gus Wiseman_, May 14 2024
%E A372686 a(26)-a(36) from _Pontus von Brömssen_, May 15 2024