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%I #30 Jan 27 2023 19:00:52
%S 1,3,7,15,31,63,127,255,511,8191,16383,32767,65535,262143,524287,
%T 16777215,33554431,134217727,268435455,2147483647,4294967295,
%U 8589934591,17179869183,34359738367,68719476735,137438953471,549755813887,562949953421311
%N Mersenne numbers for which the product of the digits is not zero.
%C These are all the Mersenne numbers for which no digit is 0. The indices of these numbers are A007377.
%H Arkadiusz Wesolowski, <a href="/A117060/b117060.txt">Table of n, a(n) for n = 1..35</a>
%F a(n) = 2^(A007377(n)) - 1. [_Arkadiusz Wesolowski_, Jun 28 2011]
%t Flatten[Table[If[First@Union@IntegerDigits[2^n - 1] != 0, 2^n - 1, {}], {n, 100}]] (* _Arkadiusz Wesolowski_, Sep 04 2011 *)
%o (Perl) use bignum;
%o for(1..99) {
%o if((1<<$_) =~ /^[1-9]+$/) {
%o print(((1 << $_) - 1) . ", ")
%o }
%o } # _Charles R Greathouse IV_, Jun 30 2011
%o (PARI) for(n=1, 99, if(vecmin(eval(Vec(Str(2^n)))), print1(2^n-1", "))) \\ _Charles R Greathouse IV_, Jun 30 2011
%Y Cf. A000225, A007377.
%K base,nonn
%O 1,2
%A Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006
%E Offset corrected by _Arkadiusz Wesolowski_, Jun 28 2011
%E Corrected by _Arkadiusz Wesolowski_, Oct 03 2011
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