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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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Last modified June 22 12:24 EDT 2017. Contains 288613 sequences.