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 A117060 Mersenne numbers for which the product of the digits is not zero. 1
 1, 3, 7, 15, 31, 63, 127, 255, 511, 8191, 16383, 32767, 65535, 262143, 524287, 16777215, 33554431, 134217727, 268435455, 2147483647, 4294967295, 8589934591, 17179869183, 34359738367, 68719476735, 137438953471, 549755813887, 562949953421311 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These are all the Mersenne numbers for which no digit is 0. The indices of these numbers are: 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. Are there more? I didn't find any above 2^86 - 1. LINKS Arkadiusz Wesolowski, Table of n, a(n) for n = 1..35 FORMULA a(n) = 2^(A007377(n)) - 1. [Arkadiusz Wesolowski, Jun 28 2011] MATHEMATICA Flatten[Table[If[First@Union@IntegerDigits[2^n - 1] != 0, 2^n - 1, {}], {n, 100}]] (* Arkadiusz Wesolowski, Sep 04 2011 *) PROG (Perl) use bignum; for(1..99) {   if((1<<\$_) =~ /^[1-9]+\$/) {     print(((1 << \$_) - 1) . ", ")   } } # Charles R Greathouse IV, Jun 30 2011 (PARI) for(n=1, 99, if(vecmin(eval(Vec(Str(2^n)))), print1(2^n-1", "))) \\ Charles R Greathouse IV, Jun 30 2011 CROSSREFS Cf. A000225, A007377. Sequence in context: A255047 A168604 A123121 * A178460 A057613 A174743 Adjacent sequences:  A117057 A117058 A117059 * A117061 A117062 A117063 KEYWORD base,nonn AUTHOR Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006 EXTENSIONS Offset corrected by Arkadiusz Wesolowski, Jun 28 2011 Corrected by Arkadiusz Wesolowski, Oct 03 2011 STATUS approved

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