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%I #13 Jan 28 2020 16:13:24
%S 1,3,7,56,617,58886,495747595,39580716961708594,
%T 295807174575157636751575471708593,
%U 19580717457515767633229292922435653422929292233676751575471708592
%N a(1) = 1; for n>1, a(n+1) is the least number such that there are a(n) palindromes between a(n) and a(n+1) with both ends excluded.
%H Andrew Howroyd, <a href="/A100772/b100772.txt">Table of n, a(n) for n = 1..14</a>
%e a(3)= 7, a(4) = 56 as there are 7 palindromes between 7 and 56: (8,9,11,22,33,44,55).
%t Nest[Append[#, Block[{k = 0}, Catch@ Do[Which[k == #[[-1]], Throw[i]; Break[], PalindromeQ@ i, k++, True, Nothing], {i, #[[-1]] + 1, Infinity}]]] &, {1}, 5] (* _Michael De Vlieger_, Jan 28 2020 *)
%o (PARI) \\ Requires A002113.
%o a(n)={my(k=1, t=0); for(i=1, n, t=1+A002113(k); k += t + (t<10)); t} \\ _Andrew Howroyd_, Jan 27 2020
%Y Cf. A002113 (palindromes in base 10).
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Nov 28 2004
%E a(5)-a(7) from _Ray Chandler_, Dec 10 2004
%E a(8) from _Donovan Johnson_, Dec 03 2009
%E Terms a(9) and beyond from _Andrew Howroyd_, Jan 27 2020
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