login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A068588 Treated as strings, n and its reversal are substrings of 2^n. 1
6, 10, 44, 49, 60, 67, 190, 191, 226, 252, 321, 373, 430, 521, 551, 609, 613, 660, 666, 680, 697, 703, 727, 730, 742, 750, 777, 805, 810, 838, 842, 847, 851, 861, 879, 889, 905, 913, 919, 920, 944, 949, 950, 959, 968, 973, 982 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For an arithmetical function f whose range is a set of integers, call n a "fixated point" of f if, treated as strings, n and its reversal are both substrings of f(n). a(n) above lists the fixated points of f(n) = 2^n. In general, the faster f(n) grows with respect to n, the more digits f(n) will have as compared with n, hence the likelier it is to contain n and n' as substrings. Thus it is more interesting to consider f(n) which grows slowly with respect to n. One such function is given by f(n) = Prime(n). The only fixated points of f not exceeding 107 are 7 and 6460. Are there any more such points?

LINKS

Table of n, a(n) for n=1..47.

Pe, J., Fixated Points of Arithmetical Functions [Link updated by Jason G. Wurtzel, Sep 07 2010]

EXAMPLE

2^49 = 562949953421312 in which both 49 and its reversal 94 appear as substrings, so 49 belongs to the sequence.

MATHEMATICA

Do[m = 2^n; If[StringPosition[ToString[m], ToString[n]] != {} && StringPosition[ToString[m], ToString[FromDigits[Reverse[IntegerDigits[n]]]]] != {}, Print[n]], {n, 1, 1000}]

CROSSREFS

Sequence in context: A132095 A332441 A153328 * A083333 A032359 A115917

Adjacent sequences:  A068585 A068586 A068587 * A068589 A068590 A068591

KEYWORD

nonn,base

AUTHOR

Joseph L. Pe, Mar 27 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 30 20:19 EDT 2020. Contains 337440 sequences. (Running on oeis4.)