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 A068588 #12 Sep 02 2025 04:09:51
%S A068588 6,10,44,49,60,67,190,191,226,252,321,373,430,521,551,609,613,660,666,
%T A068588 680,697,703,727,730,742,750,777,805,810,838,842,847,851,861,879,889,
%U A068588 905,913,919,920,944,949,950,959,968,973,982
%N A068588 Treated as strings, n and its reversal are substrings of 2^n.
%C A068588 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?
%H A068588 Joseph L. Pe, <a href="https://web.archive.org/web/20081118130509/http://www.geocities.com/windmill96/enlightened/fixated.html">Fixated Points of Arithmetical Functions</a>.
%e A068588 2^49 = 562949953421312 in which both 49 and its reversal 94 appear as substrings, so 49 belongs to the sequence.
%t A068588 Do[m = 2^n; If[StringPosition[ToString[m], ToString[n]] != {} && StringPosition[ToString[m], ToString[FromDigits[Reverse[IntegerDigits[n]]]]] != {}, Print[n]], {n, 1, 1000}]
%t A068588 sbsQ[n_]:=Module[{c=IntegerDigits[2^n]},SequenceCount[c,IntegerDigits[n]]>0 && SequenceCount[c,IntegerDigits[IntegerReverse[n]]]>0]; Select[Range[1000],sbsQ] (* _Harvey P. Dale_, May 08 2022 *)
%K A068588 nonn,base,changed
%O A068588 1,1
%A A068588 _Joseph L. Pe_, Mar 27 2002