Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Feb 22 2020 07:03:11
%S 7,23,52,54,86,303,389,5112,60392,87491,94788,97115,616916,672938066
%N Self-locating numbers within the decimal expansion of log(2): strings k beginning at position k (first digit after decimal point is position 2).
%C a(15) > 10^9.
%C 52 and 54 are self-locating numbers which appear consecutively in log(2) = 0.693...5254....
%e For 0.693147..., if 6 appears at position 2, then 7 appears at position 7.
%t dlog2 = RealDigits[Log[2], 10, 1000010][[1]]; Select[Range[2, 1000000], FromDigits[Take[dlog2, {# - 1, # - 2 + IntegerLength[#]}]] == # &] (* _Vaclav Kotesovec_, Feb 18 2020 *)
%Y Decimal expansion of log(2): A002162.
%Y Self-locating digits of Pi: A057679, A153220.
%K nonn,base,more
%O 1,1
%A _S. Alwin Mao_, Feb 14 2020