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A164022
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a(n) = the smallest prime that, when written in binary, starts with the substring of n in binary.
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2
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2, 2, 3, 17, 5, 13, 7, 17, 19, 41, 11, 97, 13, 29, 31, 67, 17, 37, 19, 41, 43, 89, 23, 97, 101, 53, 109, 113, 29, 61, 31, 131, 67, 137, 71, 73, 37, 307, 79, 163, 41, 337, 43, 89, 181, 373, 47, 97, 197, 101, 103, 211, 53, 109, 223, 113, 229, 233, 59, 241, 61, 251, 127, 257
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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EXAMPLE
| 4 in binary is 100. Looking at the binary numbers that begin with 100: 100 = 4 in decimal is composite; 1000 = 8 in decimal is composite; 1001 = 9 in decimal is composite; 10000 = 16 in decimal is composite. But 10001 = 17 in decimal is prime. So a(4) = 17.
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MAPLE
| A164022 := proc(n) dgs2 := convert(n, base, 2) ; ldgs := nops(dgs2) ; for i from 1 do p := ithprime(i) ; if p >= n then pdgs := convert(p, base, 2) ; if [op(nops(pdgs)+1-ldgs.. nops(pdgs), pdgs)] = dgs2 then RETURN( p) ; fi; fi; od: end: seq(A164022(n), n=1..120) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 13 2009]
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CROSSREFS
| Cf. A164023
Sequence in context: A060790 A109843 A184840 * A089751 A137909 A035796
Adjacent sequences: A164019 A164020 A164021 * A164023 A164024 A164025
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KEYWORD
| base,nonn
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AUTHOR
| Leroy Quet, Aug 08 2009
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EXTENSIONS
| Corrected terms a(1) and a(2) (with help from Ray Chandler) Leroy Quet, Aug 16 2009
Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 13 2009
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