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Last n-digit string to appear as the first n digits of a positive power of 2.
1

%I #8 Sep 10 2023 09:08:12

%S 9,97,982,7629,95367,997432,9313225,95367431

%N Last n-digit string to appear as the first n digits of a positive power of 2.

%C a(n) = floor(f(n) / 10^(floor(log_10(f(n))) - n + 1)) where f(n) = 2^A155700(n). (I.e., a(n) is the number composed of the first n digits of 2^A155700(n).)

%e The powers of 2 having at least 2 digits are 16, 32, 64, 128, 256, ...; discarding all but their first 2 digits yields the sequence 16, 32, 64, 12, 25, ..., in which all 90 of the possible 2-digit numbers (10 through 99) eventually appear; the last to appear is 97 (at 2^279 = 9.713...*10^83), so a(2) = 97.

%Y Cf. A000079, A155700.

%K nonn,base,more

%O 1,1

%A _Jon E. Schoenfield_, Jan 25 2009