A088249 Smallest palindromic prime beginning with the n-th prime, or 0 if no such prime exists.

2, 3, 5, 7, 11, 131, 17471, 191, 0, 0, 313, 373, 0, 0, 0, 0, 0, 0, 0, 71317, 73037, 797, 0, 0, 97379, 101, 10301, 1074701, 1092901, 11311, 12721, 131, 1371731, 13931, 1490941, 151, 1572751, 16361, 1670761, 1730371, 17971, 181, 191, 19391, 1970791, 19991

Offset

1,1

Comments

Conjecture: Except for n=1 and 3, a(n) = 0 iff prime(n) has Most Significant digit one among (2,4,5,6,8).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(7) = 17471, prime(7) = 17. a(9) = 0, prime(9) = 23 and no such prime exists.

Maple

revdigs:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
pali:= proc(n) local d;
    d:= ilog10(n);
    n*10^d + revdigs(floor(n/10));
end proc:
f:= proc(n) local L, Lp, x, cand, d;
  L:= convert(n, base, 10);
  if not member(L[-1], [1, 3, 7, 9]) then return 0 fi;
  for d from nops(L) to 0 by -1 do
    if L[1..d] = ListTools:-Reverse(L[1..d]) then
      Lp:= [op(ListTools:-Reverse(L[d+1..-1])), op(L)];
      cand:= add(Lp[i]*10^(i-1), i=1..nops(Lp));
      if isprime(cand) then return cand fi
    fi
  od;
  for d from 1 do
    for x from 0 to 10^d-1 do
      cand:= pali(10^d*n+x);
      if isprime(cand) then return cand fi;
    od;
  od
end proc:
f(2):= 2: f(5):= 5:
map(f @ ithprime, [$1..100]); # Robert Israel, Aug 06 2020

Crossrefs

Sequence in context: A084836 A062351 A185267 * A241724 A186449 A046480

Adjacent sequences: A088246 A088247 A088248 * A088250 A088251 A088252

Keyword

base,easy,nonn,look

Author

Amarnath Murthy, Sep 26 2003

Extensions

More terms from Giovanni Resta, Feb 07 2006

Status

approved