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A372684
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Least k such that prime(k) >= 2^n.
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19
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1, 3, 5, 7, 12, 19, 32, 55, 98, 173, 310, 565, 1029, 1901, 3513, 6543, 12252, 23001, 43391, 82026, 155612, 295948, 564164, 1077872, 2063690, 3957810, 7603554, 14630844, 28192751, 54400029, 105097566, 203280222, 393615807, 762939112, 1480206280, 2874398516, 5586502349
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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The numbers prime(a(n)) together with their binary expansions and binary indices begin:
2: 10 ~ {2}
5: 101 ~ {1,3}
11: 1011 ~ {1,2,4}
17: 10001 ~ {1,5}
37: 100101 ~ {1,3,6}
67: 1000011 ~ {1,2,7}
131: 10000011 ~ {1,2,8}
257: 100000001 ~ {1,9}
521: 1000001001 ~ {1,4,10}
1031: 10000000111 ~ {1,2,3,11}
2053: 100000000101 ~ {1,3,12}
4099: 1000000000011 ~ {1,2,13}
8209: 10000000010001 ~ {1,5,14}
16411: 100000000011011 ~ {1,2,4,5,15}
32771: 1000000000000011 ~ {1,2,16}
65537: 10000000000000001 ~ {1,17}
131101: 100000000000011101 ~ {1,3,4,5,18}
262147: 1000000000000000011 ~ {1,2,19}
524309: 10000000000000010101 ~ {1,3,5,20}
1048583: 100000000000000000111 ~ {1,2,3,21}
2097169: 1000000000000000010001 ~ {1,5,22}
4194319: 10000000000000000001111 ~ {1,2,3,4,23}
8388617: 100000000000000000001001 ~ {1,4,24}
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MATHEMATICA
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Table[PrimePi[If[n==1, 2, NextPrime[2^n]]], {n, 30}]
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PROG
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(PARI) a(n) = primepi(nextprime(2^n)); \\ Michel Marcus, May 31 2024
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CROSSREFS
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The opposite (greatest k such that prime(k) <= 2^n) is A007053.
Positions of first appearances in A035100.
The distance from prime(a(n)) to 2^n is A092131.
For primes between powers of 2:
For squarefree numbers between powers of 2:
For squarefree numbers between primes:
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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