A084122 Numbers k such that k*prime(k) is a palindrome.

1, 2, 5, 12, 16, 3623, 4119, 618725, 708567, 1498739, 2762990591

Offset

1,2

Comments

a(12) > 3.7*10^12. - Giovanni Resta, Jun 28 2013

Links

Table of n, a(n) for n=1..11.

Example

4119 is in the sequence since the 4119th prime is 39119 and 4199*39119 = 161131161 is a palindrome.

Maple

ispal:= proc(n) local L;
  L:= convert(n, base, 10);
  L = ListTools:-Reverse(L);
end proc:
R:= NULL: count:= 0: p:= 1:
for k from 1 while count < 11 do
  p:= nextprime(p);
  if ispal(k*p) then R:= R, k; count:= count+1 fi
od:
R; # Robert Israel, Feb 22 2023

Mathematica

palQ[n_]:=FromDigits[Reverse[IntegerDigits[n]]]==n; t={}; Do[If[palQ[Prime[n]*n], AppendTo[t, n]], {n, 15*10^5}]; t (* Jayanta Basu, May 11 2013 *)

Prog

(PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d); \\ A002113
isok(k) = ispal(k*prime(k)) \\ Alexandru Petrescu, Feb 22 2023
(Python)
from sympy import sieve
def ok(n): return n and (s := str(n*sieve[n])) ==  s[::-1]
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Feb 22 2023

Crossrefs

Cf. A002113, A033286, A084121, A084123.

Sequence in context: A102718 A219954 A066267 * A042143 A042467 A024465

Adjacent sequences: A084119 A084120 A084121 * A084123 A084124 A084125

Keyword

base,nonn,more

Author

Giovanni Resta, May 14 2003

Status

approved