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 A036229 Smallest n-digit prime containing only digits 1 or 2 or -1 if no such prime exists. 25
 2, 11, 211, 2111, 12211, 111121, 1111211, 11221211, 111112121, 1111111121, 11111121121, 111111211111, 1111111121221, 11111111112221, 111111112111121, 1111111112122111, 11111111111112121, 111111111111112111, 1111111111111111111, 11111111111111212121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is conjectured that such a prime always exists. a(2), a(19), a(23), etc. are the prime repunits (A004023). a(1000) = (10^n-1)/9 + 111011000010. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..1000 (terms n=1..400 from Alois P. Heinz) Robert G. Wilson v, Comments and first 100 terms MATHEMATICA Do[p = (10^n - 1)/9; k = 0; While[ ! PrimeQ[p], k++; p = FromDigits[ PadLeft[ IntegerDigits[ k, 2], n] + 1]]; Print[p], {n, 1, 20}] Table[Min[Select[ FromDigits/@Tuples[{1, 2}, n], PrimeQ]], {n, 20}] (* Harvey P. Dale, Feb 05 2014 *) PROG (Python) from sympy import isprime def A036229(n): k, r, m = (10**n-1)//9, 2**n-1, 0 while m <= r: t = k+int(bin(m)[2:]) if isprime(t): return t m += 1 return -1 # Chai Wah Wu, Aug 18 2021 CROSSREFS Cf. A036937, A068086. Sequence in context: A070256 A356523 A020450 * A104337 A283512 A214217 Adjacent sequences: A036226 A036227 A036228 * A036230 A036231 A036232 KEYWORD nonn,base,nice AUTHOR G. L. Honaker, Jr. EXTENSIONS Edited by N. J. A. Sloane and Robert G. Wilson v, May 03 2002 Escape clause added by Chai Wah Wu, Aug 18 2021 STATUS approved

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Last modified April 20 00:58 EDT 2024. Contains 371798 sequences. (Running on oeis4.)