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A117060
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Mersenne numbers for which the product of the digits is not zero.
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1
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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; internal format)
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OFFSET
| 1,2
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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.
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LINKS
| Arkadiusz Wesolowski, Table of n, a(n) for n = 1..35
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FORMULA
| a(n) = 2^(A007377(n)) - 1. [Arkadiusz Wesolowski, Jun 28 2011]
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MATHEMATICA
| Flatten[Table[If[First@Union@IntegerDigits[2^n - 1] != 0, 2^n - 1, {}], {n, 100}]] (* Arkadiusz Wesolowski, Sep 04 2011 *)
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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
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CROSSREFS
| Cf. A000225, A007377.
Sequence in context: A126646 A000225 A123121 * A178460 A057613 A174743
Adjacent sequences: A117057 A117058 A117059 * A117061 A117062 A117063
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KEYWORD
| base,nonn
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AUTHOR
| Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006
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EXTENSIONS
| Offset corrected by Arkadiusz Wesolowski, Jun 28 2011
Corrected by Arkadiusz Wesolowski, Oct 03 2011
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