This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372684 #15 Jun 05 2024 08:53:05
%S A372684 1,3,5,7,12,19,32,55,98,173,310,565,1029,1901,3513,6543,12252,23001,
%T A372684 43391,82026,155612,295948,564164,1077872,2063690,3957810,7603554,
%U A372684 14630844,28192751,54400029,105097566,203280222,393615807,762939112,1480206280,2874398516,5586502349
%N A372684 Least k such that prime(k) >= 2^n.
%F A372684 a(n>1) = A007053(n) + 1.
%F A372684 a(n) = A000720(A104080(n)).
%F A372684 prime(a(n)) = A104080(n).
%F A372684 prime(a(n)) - 2^n = A092131(n).
%e A372684 The numbers prime(a(n)) together with their binary expansions and binary indices begin:
%e A372684 2: 10 ~ {2}
%e A372684 5: 101 ~ {1,3}
%e A372684 11: 1011 ~ {1,2,4}
%e A372684 17: 10001 ~ {1,5}
%e A372684 37: 100101 ~ {1,3,6}
%e A372684 67: 1000011 ~ {1,2,7}
%e A372684 131: 10000011 ~ {1,2,8}
%e A372684 257: 100000001 ~ {1,9}
%e A372684 521: 1000001001 ~ {1,4,10}
%e A372684 1031: 10000000111 ~ {1,2,3,11}
%e A372684 2053: 100000000101 ~ {1,3,12}
%e A372684 4099: 1000000000011 ~ {1,2,13}
%e A372684 8209: 10000000010001 ~ {1,5,14}
%e A372684 16411: 100000000011011 ~ {1,2,4,5,15}
%e A372684 32771: 1000000000000011 ~ {1,2,16}
%e A372684 65537: 10000000000000001 ~ {1,17}
%e A372684 131101: 100000000000011101 ~ {1,3,4,5,18}
%e A372684 262147: 1000000000000000011 ~ {1,2,19}
%e A372684 524309: 10000000000000010101 ~ {1,3,5,20}
%e A372684 1048583: 100000000000000000111 ~ {1,2,3,21}
%e A372684 2097169: 1000000000000000010001 ~ {1,5,22}
%e A372684 4194319: 10000000000000000001111 ~ {1,2,3,4,23}
%e A372684 8388617: 100000000000000000001001 ~ {1,4,24}
%t A372684 Table[PrimePi[If[n==1,2,NextPrime[2^n]]],{n,30}]
%o A372684 (PARI) a(n) = primepi(nextprime(2^n)); \\ _Michel Marcus_, May 31 2024
%Y A372684 The opposite (greatest k such that prime(k) <= 2^n) is A007053.
%Y A372684 Positions of first appearances in A035100.
%Y A372684 The distance from prime(a(n)) to 2^n is A092131.
%Y A372684 Counting zeros instead of all bits gives A372474, firsts of A035103.
%Y A372684 Counting ones instead of all bits gives A372517, firsts of A014499.
%Y A372684 For primes between powers of 2:
%Y A372684 - sum A293697
%Y A372684 - length A036378
%Y A372684 - min A104080 or A014210
%Y A372684 - max A014234, delta A013603
%Y A372684 For squarefree numbers between powers of 2:
%Y A372684 - sum A373123
%Y A372684 - length A077643, run-lengths of A372475
%Y A372684 - min A372683, delta A373125, indices A372540
%Y A372684 - max A372889, delta A373126, indices A143658
%Y A372684 For squarefree numbers between primes:
%Y A372684 - sum A373197
%Y A372684 - length A373198 = A061398 - 1
%Y A372684 - min A000040
%Y A372684 - max A112925, opposite A112926
%Y A372684 Cf. A000120, A029837, A029931, A030190, A049095, A069010, A070939, A077641, A080791, A211997.
%K A372684 nonn
%O A372684 1,2
%A A372684 _Gus Wiseman_, May 30 2024
%E A372684 More terms from _Michel Marcus_, May 31 2024