cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A121319 a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k must have at least n digits (cf. A113627).

Original entry on oeis.org

14, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 1075353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736
Offset: 1

Views

Author

Tanya Khovanova, Aug 25 2006

Keywords

Examples

			2^14 = 16384 and 14 end with the same single digit 4, thus a(1) = 14.

Links

Crossrefs

Cf. A007185, A016090, A003226, A035383, A064540, A064541, A109405.

Programs

  • Mathematica
    f[n_] := Block[{k = If[n == 1, 2, 10], m = 10^n}, While[ PowerMod[2, k, m] != Mod[k, m], k += 2]; k]; Do[ Print@f@n, {n, 9}] (* Robert G. Wilson v *)
  • PARI
    A121319(n) = { local(k,tn); tn=10^n ; forstep(k=2,1000000000,2, if ( k % tn == (2^k) % tn, return(k) ; ) ; ) ; return(0) ; } { for(n = 1,13, print( A121319(n)) ; ) ; } \\ R. J. Mathar, Aug 27 2006

Formula

If A109405(n) has n digits, a(n) = A109405(n), otherwise a(n) = A109405(n) + 10^n. - Max Alekseyev, May 05 2007

Extensions

a(6)-a(9) from Robert G. Wilson v and Jon E. Schoenfield, Aug 26 2006
a(10) from Robert G. Wilson v, Sep 26 2006
a(11)-a(16) from Alexander Adamchuk, Jan 28 2007
a(16) corrected by Max Alekseyev, Apr 12 2007

A109405 a(2) = 36; for n >= 3, a(n) = 2^a(n-1) mod 10^n.

Original entry on oeis.org

36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 75353432948736, 5075353432948736, 15075353432948736, 615075353432948736
Offset: 2

Views

Author

N. J. A. Sloane, following email from Max Alekseyev, May 06 2007

Keywords

Comments

Decimal digits read backwards form A133612.
Related to but different from A064541 and A121319.

Links

Crossrefs

Same as A113627 except for the initial term (14). - Max Alekseyev, May 11 2007

Programs

  • Mathematica
    a = 36; For[n = 3, n < 25, n++, a = PowerMod[2, a, 10^n]; Print[a]] (* Stefan Steinerberger, May 25 2007 *)
nxt[{n_,a_}]:={n+1,PowerMod[2,a,10^(n+1)]}; NestList[nxt,{2,36},20][[All,2]] (* Harvey P. Dale, Jan 22 2023 *)

Extensions

More terms from Stefan Steinerberger, May 25 2007

A206636 a(n) = 2^^(n+2) modulo 10^n, where ^^ denotes a power tower (see A133612).

Original entry on oeis.org

6, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 75353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736, 98615075353432948736, 8098615075353432948736
Offset: 1

Views

Author

Marco Ripà, Feb 10 2012

Keywords

Comments

Backward concatenation of A133612.
For all m>n+1, 2^^m == 2^^(n+2) (mod 10^n). Hence, each term represents the trailing decimal digits of 2^^m for every sufficiently large m.

References

  • M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6.

Links

Crossrefs

Cf. A133612, A113627, A109405, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A183613, A144539, A144540, A144541, A144542, A144543, A144544.

Programs

  • Mathematica
    (* first load all lines of Super Power Mod by Ilan Vardi from the hyper-link, then *) $RecursionLimit = 2^14;  a[n_] := SuperPowerMod[2, n +2, 10^n]; Array[a, 22] (* Robert G. Wilson v, Apr 20 2020 *)

Formula

a(n) = A014221(n+3) mod (10^n).
For n>1, a(n) = 2^a(n-1) mod 10^n.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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