A186698 Next prime after n-th positive palindrome.

2, 3, 5, 5, 7, 7, 11, 11, 11, 13, 23, 37, 47, 59, 67, 79, 89, 101, 103, 113, 127, 137, 149, 157, 163, 173, 191, 193, 211, 223, 223, 233, 251, 257, 263, 277, 283, 293, 307, 317, 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

Offset

1,1

Comments

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

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n) = A151800(A002113(n+1)). - Michael S. Branicky, Jul 10 2024

Maple

digrev:= proc(x) option remember; local t;
   t:= x mod 10;
   t*10^ilog10(x)+procname((x-t)/10)
end proc:
for x from 0 to 9 do digrev(x):= x od:
N:=6;
Pals:= $1..9:
for d from 2 to N do
  if d::even then
    m:= d/2;
    Pals:= Pals, seq(n*10^m + digrev(n), n=10^(m-1)..10^m-1);
  else
    m:= (d-1)/2;
    Pals:= Pals, seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1);
  fi
od:
Pals:=[Pals]:
map(nextprime, Pals); # Robert Israel, Nov 04 2015

Mathematica

NextPrime[Select[Range[700], PalindromeQ]] (* Harvey P. Dale, Jan 31 2024 *)

Prog

(Python)
from sympy import nextprime
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

Crossrefs

Cf. A014208, A186697, A151800, A002113.

Sequence in context: A159477 A268101 A123318 * A234345 A111060 A082432

Adjacent sequences: A186695 A186696 A186697 * A186699 A186700 A186701

Keyword

nonn,base

Author

Harvey P. Dale, Feb 25 2011

Status

approved