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Numbers k such that the decimal expansion of 3^k contains no 9.
8

%I #20 Sep 08 2022 08:45:31

%S 0,1,3,4,5,7,8,11,12,16,19,20,21,29,32,56

%N Numbers k such that the decimal expansion of 3^k contains no 9.

%C I conjecture that 56 is the last term.

%t Join[{0}, Select[ Range@10000, FreeQ[ IntegerDigits[3^# ], 9] &]]

%o (Magma) [n: n in [0..1000] | not 9 in Intseq(3^n) ]; // _Vincenzo Librandi_, May 06 2015

%Y Numbers k such that the decimal expansion of 3^k contains no m: A030700 (m=0), A131627 (m=1), A131625 (m=2), A131629 (m=3), A131618 (m=4), A131617 (m=5), A131616 (m=6), A131615 (m=7), A131614 (m=8), this sequence (m=9).

%Y Cf. A007377.

%K base,fini,nonn

%O 1,3

%A _Shyam Sunder Gupta_, Sep 01 2007

%E Adapted Mma and initial 0 added by _Vincenzo Librandi_, May 06 2015