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A186698 Next prime after n-th positive palindrome.

%I A186698 #23 Jul 14 2024 08:32:32
%S A186698 2,3,5,5,7,7,11,11,11,13,23,37,47,59,67,79,89,101,103,113,127,137,149,
%T A186698 157,163,173,191,193,211,223,223,233,251,257,263,277,283,293,307,317,
%U A186698 331,337,347,359,367,379,389,397,409,419,431,439,449,457,467,479,487,499,509,521,541,541,547,557,569,577,587,599,607,617,631,641,647
%N A186698 Next prime after n-th positive palindrome.
%C A186698 There are infinitely many n for which a(n+1) = a(n).  For example, when 10^k + 1 is composite, 10^k - 1 and 10^k + 1 are successive palindromes which have the same next prime. - _Robert Israel_, Nov 04 2015
%H A186698 Chai Wah Wu, <a href="/A186698/b186698.txt">Table of n, a(n) for n = 1..10000</a>
%F A186698 a(n) = A151800(A002113(n+1)). - _Michael S. Branicky_, Jul 10 2024
%p A186698 digrev:= proc(x) option remember; local t;
%p A186698    t:= x mod 10;
%p A186698    t*10^ilog10(x)+procname((x-t)/10)
%p A186698 end proc:
%p A186698 for x from 0 to 9 do digrev(x):= x od:
%p A186698 N:=6;
%p A186698 Pals:= $1..9:
%p A186698 for d from 2 to N do
%p A186698   if d::even then
%p A186698     m:= d/2;
%p A186698     Pals:= Pals, seq(n*10^m + digrev(n), n=10^(m-1)..10^m-1);
%p A186698   else
%p A186698     m:= (d-1)/2;
%p A186698     Pals:= Pals, seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1);
%p A186698   fi
%p A186698 od:
%p A186698 Pals:=[Pals]:
%p A186698 map(nextprime,Pals); # _Robert Israel_, Nov 04 2015
%t A186698 NextPrime[Select[Range[700],PalindromeQ]] (* _Harvey P. Dale_, Jan 31 2024 *)
%o A186698 (Python)
%o A186698 from sympy import nextprime
%o A186698 def A186698(n): return int(nextprime((c:=n+1-x)*x+int(str(c)[-2::-1] or 0) if n+1<(x:=10**(len(str(n+1>>1))-1))+(y:=10*x) else (c:=n+1-y)*y+int(str(c)[::-1] or 0))) # _Chai Wah Wu_, Jul 10 2024
%Y A186698 Cf. A014208, A186697, A151800, A002113.
%K A186698 nonn,base
%O A186698 1,1
%A A186698 _Harvey P. Dale_, Feb 25 2011