A084122 - OEIS

%I #42 Feb 28 2023 06:03:09

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

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

%C a(12) > 3.7*10^12. - _Giovanni Resta_, Jun 28 2013

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

%p ispal:= proc(n) local L;

%p   L:= convert(n,base,10);

%p   L = ListTools:-Reverse(L);

%p end proc:

%p R:= NULL: count:= 0: p:= 1:

%p for k from 1 while count < 11 do

%p   p:= nextprime(p);

%p   if ispal(k*p) then R:= R,k; count:= count+1 fi

%p od:

%p R; # _Robert Israel_, Feb 22 2023

%t 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 *)

%o (PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d); \\ A002113

%o isok(k) = ispal(k*prime(k)) \\ _Alexandru Petrescu_, Feb 22 2023

%o (Python)

%o from sympy import sieve

%o def ok(n): return n and (s := str(n*sieve[n])) ==  s[::-1]

%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Feb 22 2023

%Y Cf. A002113, A033286, A084121, A084123.

%K base,nonn,more

%O 1,2

%A _Giovanni Resta_, May 14 2003