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 A331630 #39 Mar 03 2023 10:28:45
%S A331630 77,76923077,76923076923077,76923076923076923077,
%T A331630 76923076923076923076923077,76923076923076923076923076923077,
%U A331630 76923076923076923076923076923076923077,76923076923076923076923076923076923076923077
%N A331630 Numbers M such that 23 * M = 1M1, where 1M1 denotes the concatenation of 1, M and 1.
%C A331630 There are only 15 numbers k such that there exist numbers M_k which, when 1 is placed at both ends of M_k, the number M_k is multiplied by k; 23 is the second such integer, so 23 = A329914(2), and a(1) = A329915(2) = 77; hence, the terms of this sequence form the infinite set {M_23}.
%C A331630 Every term M = a(n) has q = 6*n-4 digits, and 10^(q+1)+1 that has 6*n-4 zeros in its decimal expansion is equal to 13 * M, so M is a divisor of 10^(6*n-3)+1. Example: a(2) = 76923077 has 8 digits and 13 * 76923077 = 1000000001 that has 8 zeros in its decimal expansion.
%D A331630 D. Wells, 112359550561797732809 entry, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1997, p. 196.
%H A331630 Colin Barker, <a href="/A331630/b331630.txt">Table of n, a(n) for n = 1..150</a>
%H A331630 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1000001,-1000000).
%F A331630 a(n) = (10^(6*n-3)+1)/13 for n >= 1.
%F A331630 From _Colin Barker_, Jan 25 2020: (Start)
%F A331630 G.f.: 77*x*(1 - 1000*x) / ((1 - x)*(1 - 1000000*x)).
%F A331630 a(n) = 1000001*a(n-1) - 1000000*a(n-2) for n>2.
%F A331630 a(n) = (1000 + 1000^(2*n))/13000 for n>0.
%F A331630 (End)
%F A331630 E.g.f.: exp(x)*(1000 + exp(999999*x))/13000 - 77/1000. - _Stefano Spezia_, Jan 26 2020
%e A331630 23 * 77 = 1771, hence 77 is a term.
%e A331630 23 * 76923076923077 = 1(76923076923077)1, and 76923076923077 is another term.
%p A331630 seq((10^(6*m-3)+1)/13, m=1..15);
%t A331630 Array[(10^(6 # - 3) + 1)/13 &, 9] (* _Michael De Vlieger_, Jan 24 2020 *)
%t A331630 LinearRecurrence[{1000001,-1000000},{77,76923077},10] (* _Harvey P. Dale_, Mar 03 2023 *)
%o A331630 (PARI) vector(9, n, (10^(6*n-3)+1)/13) \\ _Michel Marcus_, Jan 25 2020
%o A331630 (PARI) Vec(77*x*(1 - 1000*x) / ((1 - x)*(1 - 1000000*x)) + O(x^10)) \\ _Colin Barker_, Jan 25 2020
%o A331630 (PARI) apply( {A331630(n)=10^(6*n-3)\/13}, [1..9]) \\ _M. F. Hasler_, Jan 26 2020, following Michel Marcus
%Y A331630 Subsequence of A116436.
%Y A331630 Cf. A329914, A329915, A095372 \ {1} (similar for k = 21).
%K A331630 nonn,base,easy
%O A331630 1,1
%A A331630 _Bernard Schott_, Jan 23 2020