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 A103662 Smallest power with base>1 and exponent n whose decimal representation doesn't contain the digit 0. 11
 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 9765625, 177147, 531441, 8192, 16384, 32768, 65536, 17179869184, 262144, 524288, 3833759992447475122176, 1582794342217312156827221746448942623537121214738891981, 341427877364219557396646723584, 94143178827, 16777216 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For statistical reasons it is conjectured that the sequence is finite. a(40), if it exists, is not known. From M. F. Hasler, Mar 08 2014 (Start): Finite means here that for some n, no such power > 1 exists. This might be the case already for n=40. Alternatively, the sequence might be defined for all n by letting a(n)=1 if no larger power exists. Then a(n)=n^A103663(n) for all n. Differs from A238938 from n=10 on. See the OEIS wiki page for further information. (End) LINKS Michel Marcus, Table of n, a(n) for n = 0..39 M. F. Hasler, Zeroless powers, OEIS wiki, Mar 07 2014 FORMULA a(n) = A103663(n)^n. - M. F. Hasler, Mar 08 2014 EXAMPLE base / exponent n / base^exponent 2 1 2 2 2 4 2 3 8 2 4 16 2 5 32 2 6 64 2 7 128 2 8 256 2 9 512 5 10 9765625 3 11 177147 3 12 531441 2 13 8192 2 14 16384 2 15 32768 2 16 65536 4 17 17179869184 2 18 262144 2 19 524288 12 20 3833759992447475122176 381 21 1582794342217312156827221746448942623537121214738891981 22 22 341427877364219557396646723584 3 23 94143178827 ... a(10)=9765625 because 5^10 is the smallest 10th power containing no zero in its decimal representation (2^10=1024, 3^10=59049, 4^10=1048576). PROG (PARI) A103662(n)=for(b=2, 9e9, vecmin(digits(b^n))&&return(b^n)) \\ M. F. Hasler, Mar 08 2014 CROSSREFS Cf. A103663 = smallest bases x such that x^n has a zero-less decimal representation. Sequence in context: A275076 A275064 A238938 * A180211 A275075 A275063 Adjacent sequences:  A103659 A103660 A103661 * A103663 A103664 A103665 KEYWORD nonn,fini,base AUTHOR Hugo Pfoertner, Feb 28 2005 EXTENSIONS a(21)=381^21 found by Joshua Zucker. Edited by Charles R Greathouse IV, Aug 03 2010 STATUS approved

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Last modified August 6 11:55 EDT 2020. Contains 336246 sequences. (Running on oeis4.)