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 A164022 a(n) = the smallest prime that, when written in binary, starts with the substring of n in binary. 6
 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; text; internal format)
 OFFSET 1,1 COMMENTS The argument used to prove that A018800(n) always exists applies here also. - N. J. A. Sloane, Nov 14 2014 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..20000 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. 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) ; # R. J. Mathar, Sep 13 2009 MATHEMATICA With[{s = Map[IntegerDigits[#, 2] &, Prime@ Range[10^4]]}, Table[Block[{d = IntegerDigits[n, 2]}, FromDigits[#, 2] &@ SelectFirst[s, Take[#, UpTo@ Length@ d] == d &]], {n, 64}]] (* Michael De Vlieger, Sep 23 2017 *) CROSSREFS A018800 is the base-10 analog. Row n=1 of A262365.  Cf. A108234 (number of new bits), A208241 (proper substring). Sequence in context: A109843 A341768 A184840 * A089751 A137909 A035796 Adjacent sequences:  A164019 A164020 A164021 * A164023 A164024 A164025 KEYWORD base,nonn AUTHOR Leroy Quet, Aug 08 2009 EXTENSIONS Corrected terms a(1) and a(2) (with help from Ray Chandler) Leroy Quet, Aug 16 2009 Extended by R. J. Mathar, Sep 13 2009 STATUS approved

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Last modified August 5 14:29 EDT 2021. Contains 346469 sequences. (Running on oeis4.)