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 A094776 a(n) = largest k such that the decimal representation of 2^k does not contain the digit n. 24
 86, 91, 168, 153, 107, 71, 93, 71, 78, 108 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS These values are only conjectural. The sequence could be extended to any nonnegative integer index n defining a(n) to be the largest k such that n does not appear as substring in the decimal expansion of 2^k. I conjecture that for n = 10, 11, 12, ... it continues (2000, 3020, 1942, 1465, 1859, 2507, 1950, 1849, 1850, ...). For example, curiously enough, the largest power of 2 in which the string "10" does not appear seems to be 2^2000. - M. F. Hasler, Feb 10 2023 REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 71, p. 25, Ellipses, Paris 2008. LINKS Table of n, a(n) for n=0..9. Tanya Khovanova, 86 Conjecture, T. K.'s Math Blog, Feb. 15, 2011. Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16. EXAMPLE a(0) = 86 because 2^86 = 77371252455336267181195264 is conjectured to be the highest power of 2 that doesn't contain the digit 0. MATHEMATICA f[n_] := Block[{a = {}, k = 1}, While[k < 10000, If[ Position[ Union[ IntegerDigits[ 2^k, 10]], n] == {}, AppendTo[a, k]]; k++ ]; a]; Table[ f[n][[ -1]], {n, 0, 9}] (* Robert G. Wilson v, Jun 12 2004 *) PROG (PARI) A094776(n, L=10*20^#Str(n))={forstep(k=L, 0, -1, foreach(digits(1<

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Last modified December 10 18:13 EST 2023. Contains 367717 sequences. (Running on oeis4.)