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Numbers k such that the decimal expansion of 2^k contains the substring 777.
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%I #27 Oct 26 2019 22:18:16

%S 24,40,75,152,166,179,181,191,194,199,214,230,235,260,282,296,304,311,

%T 317,323,326,332,342,345,363,370,374,390,417,424,426,443,455,468,471,

%U 474,475,483,489,490,505,512,523,524,536,540,559,567,581,584,585,588,593

%N Numbers k such that the decimal expansion of 2^k contains the substring 777.

%C The decimal expansion of 2^k ends in 7776 iff k == 40 (mod 500), so the sequence is infinite. - _Jon E. Schoenfield_, Oct 14 2019

%C Conjecture: if n > 30536, then a(n) = n + 3623. - _Chai Wah Wu_, Oct 26 2019

%H Chai Wah Wu, <a href="/A328375/b328375.txt">Table of n, a(n) for n = 1..10000</a>

%e 16777216 = 2^24.

%p q:= n-> searchtext("777", cat(2^n))>0:

%p select(q, [$1..600])[]; # _Alois P. Heinz_, Oct 26 2019

%t aQ[n_] := SequenceCount[IntegerDigits[2^n], {7, 7, 7}] > 0; Select[Range[660], aQ] (* _Amiram Eldar_, Oct 26 2019 *)

%o (Python)

%o A328375_list = [k for k in range(1000) if '777' in str(2**k)] # _Chai Wah Wu_, Oct 26 2019

%Y Cf. A007356 (contains 666), A030000 (contains n).

%K nonn,easy,base

%O 1,1

%A _Eder Vanzei_, Oct 14 2019