This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060458 #56 Mar 27 2025 15:47:39
%S A060458 8,96,992,9984,99968,999936,9999872,99999744,999999488,9999998976,
%T A060458 99999997952,999999995904,9999999991808,99999999983616,
%U A060458 999999999967232,9999999999934464,99999999999868928,999999999999737856,9999999999999475712,99999999999998951424,999999999999997902848
%N A060458 Maximum value seen in the final n decimal digits of 2^j for all values of j.
%C A060458 Consider the final n decimal digits of 2^j for all values of j. They are periodic. Sequence gives maximal value seen in these n digits.
%C A060458 With f(n) = a(n+1) - a(n), the difference f(n) - a(n) is always 8*10^n meaning that a(n) becomes its own "first differences" sequence when each term is prefixed a digit '8'. For higher order differences, the prefix 8 becomes: 8*10^n*Sum_{k=0..m-1} 9^k where m is the order. - _R. J. Cano_, May 11 2014
%H A060458 <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>.
%H A060458 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-20).
%F A060458 a(n) = 10^n - 2^n = 2^n*(5^n - 1).
%F A060458 From _Geoffrey Critzer_, Dec 15 2011: (Start)
%F A060458 a(n) = 12*a(n-1) - 20*a(n-2).
%F A060458 O.g.f.: 1/(1-10*x) - 1/(1-2*x). (End)
%F A060458 a(n) = f(n,0) where f(x,y) = Sum_{j=0..x+y-1} (2^(3*x-2*j)*binomial(x,j)). - _R. J. Cano_, May 15 2014
%F A060458 a(n) = 2^(n+2)*A003463(n). - _R. J. Cano_, Sep 25 2014
%F A060458 a(n) = 8*A016134(n-1). - _R. J. Mathar_, Mar 10 2022
%F A060458 E.g.f.: exp(2*x)*(exp(8*x) - 1). - _Elmo R. Oliveira_, Mar 26 2025
%e A060458 Maximum of the last 4 digits of powers of 2 is 9984=10000-16. It occurs at 2^254. 2^254 = 289480223.....01978282409984 (with 77 digits, last 4 ones are ...9984). The period length of the last-4-digit segment is A005054(4)=500. For n=4 period: amplitude=9984, phase=254.
%p A060458 A060458:=n->10^n-2^n: seq(A060458(n), n=1..20); # _Wesley Ivan Hurt_, Sep 25 2014
%t A060458 RecurrenceTable[{a[n] == 12 a[n - 1] - 20 a[n - 2], a[0] == 0, a[1] == 8}, a[n], {n, 1, 20}] (* _Geoffrey Critzer_, Dec 15 2011*)
%o A060458 (Sage) [10^n - 2^n for n in range(1,19)] # _Zerinvary Lajos_, Jun 05 2009
%o A060458 (PARI) a(n)=sum(j=0,n-1,2^(3*n-2*j)*binomial(n,j)) \\ _R. J. Cano_, May 15 2014
%o A060458 (Magma) [10^n-2^n : n in [1..20]]; // _Wesley Ivan Hurt_, Sep 25 2014
%o A060458 (PARI) A060458(n)=(5^n-1)<<n \\ _M. F. Hasler_, Oct 31 2014
%Y A060458 Cf. A000079, A003463, A005054, A060460, A016134.
%K A060458 base,nonn,easy
%O A060458 1,1
%A A060458 _Labos Elemer_, Apr 09 2001
%E A060458 Edited by _M. F. Hasler_, Oct 31 2014
%E A060458 More terms from _Elmo R. Oliveira_, Mar 26 2025