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 A007377 Numbers n such that the decimal expansion of 2^n contains no 0. (Formerly M0485) 52
 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^n, which seems to end with n=68. - M. F. Hasler, Mar 07 2014 Checked up to n = 10^10. - David Radcliffe, Dec 29 2015 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 David Radcliffe, Python script to search for powers with no zero digits 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 MAPLE remove(t -> has(convert(2^t, base, 10), 0), [\$0..1000]); # Robert Israel, Dec 29 2015 MATHEMATICA Do[ If[ Union[ RealDigits[ 2^n ] [[1]]] [[1]] != 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 CROSSREFS Cf. A027870, A030700, A102483. Cf. similar sequences listed in A035064. Sequence in context: A174887 A092598 A247811 * A305932 A213882 A135140 Adjacent sequences:  A007374 A007375 A007376 * A007378 A007379 A007380 KEYWORD base,nonn AUTHOR EXTENSIONS a(1) = 0 prepended by Reinhard Zumkeller, Apr 30 2013 STATUS approved

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Last modified November 18 13:22 EST 2018. Contains 317306 sequences. (Running on oeis4.)