A084122 Numbers k such that k*prime(k) is a palindrome.
1, 2, 5, 12, 16, 3623, 4119, 618725, 708567, 1498739, 2762990591
Offset: 1
Examples
4119 is in the sequence since the 4119th prime is 39119 and 4199*39119 = 161131161 is a palindrome.
Programs
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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
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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 *) -
PARI
ispal(n) = my(d=digits(n)); d == Vecrev(d); \\ A002113 isok(k) = ispal(k*prime(k)) \\ Alexandru Petrescu, Feb 22 2023
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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
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