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 A007377 Numbers k such that the decimal expansion of 2^k contains no 0. (Formerly M0485) 56
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 18, 19, 24, 25, 27, 28, 31, 32, 33, 34, 35, 36, 37, 39, 49, 51, 67, 72, 76, 77, 81, 86 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS It is an open problem of long standing to show that 86 is the last term. A027870(a(n)) = A224782(a(n)) = 0. - Reinhard Zumkeller, Apr 30 2013 See A030700 for the analog for 3^k, which seems to end with k=68. - M. F. Hasler, Mar 07 2014 Checked up to k = 10^10. - David Radcliffe, Aug 21 2022 REFERENCES J. S. Madachy, Mathematics on Vacation, Scribner's, NY, 1966, p. 126. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Table of n, a(n) for n=1..36. W. Schneider, NoZeros: Powers n^k without Digit Zero [Cached copy] Eric Weisstein's World of Mathematics, Zero R. G. Wilson, V, Letter to N. J. A. Sloane, Oct. 1993 EXAMPLE Here is 2^86, conjecturally the largest power of 2 not containing a 0: 77371252455336267181195264. - N. J. A. Sloane, Feb 10 2023 MAPLE remove(t -> has(convert(2^t, base, 10), 0), [\$0..1000]); # Robert Israel, Dec 29 2015 MATHEMATICA Do[ If[ Union[ RealDigits[ 2^n ] []] [] != 0, Print[ n ] ], {n, 1, 60000}] Select[Range@1000, First@Union@IntegerDigits[2^# ] != 0 &] Select[Range[0, 100], DigitCount[2^#, 10, 0]==0&] (* Harvey P. Dale, Feb 06 2015 *) PROG (Magma) [ n: n in [0..50000] | not 0 in Intseq(2^n) ]; // Bruno Berselli, Jun 08 2011 (Perl) use bignum; for(0..99) { if((1<<\$_) =~ /^[1-9]+\$/) { print "\$_, " } } # Charles R Greathouse IV, Jun 30 2011 (PARI) for(n=0, 99, if(vecmin(eval(Vec(Str(2^n)))), print1(n", "))) \\ Charles R Greathouse IV, Jun 30 2011 (Haskell) import Data.List (elemIndices) a007377 n = a007377_list !! (n-1) a007377_list = elemIndices 0 a027870_list -- Reinhard Zumkeller, Apr 30 2013 (Python) def ok(n): return '0' not in str(2**n) print(list(filter(ok, range(10**4)))) # Michael S. Branicky, Aug 08 2021 CROSSREFS Cf. A027870, A030700, A102483, A034293. Some similar sequences are listed in A035064. Cf. also A031142. Sequence in context: A174887 A092598 A247811 * A305932 A213882 A135140 Adjacent sequences: A007374 A007375 A007376 * A007378 A007379 A007380 KEYWORD base,nonn AUTHOR N. J. A. Sloane, Robert G. Wilson v EXTENSIONS a(1) = 0 prepended by Reinhard Zumkeller, Apr 30 2013 STATUS approved

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Last modified May 27 19:17 EDT 2023. Contains 362985 sequences. (Running on oeis4.)