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

%I A084122 #42 Feb 28 2023 06:03:09
%S A084122 1,2,5,12,16,3623,4119,618725,708567,1498739,2762990591
%N A084122 Numbers k such that k*prime(k) is a palindrome.
%C A084122 a(12) > 3.7*10^12. - _Giovanni Resta_, Jun 28 2013
%e A084122 4119 is in the sequence since the 4119th prime is 39119 and 4199*39119 = 161131161 is a palindrome.
%p A084122 ispal:= proc(n) local L;
%p A084122   L:= convert(n,base,10);
%p A084122   L = ListTools:-Reverse(L);
%p A084122 end proc:
%p A084122 R:= NULL: count:= 0: p:= 1:
%p A084122 for k from 1 while count < 11 do
%p A084122   p:= nextprime(p);
%p A084122   if ispal(k*p) then R:= R,k; count:= count+1 fi
%p A084122 od:
%p A084122 R; # _Robert Israel_, Feb 22 2023
%t A084122 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 A084122 (PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d); \\ A002113
%o A084122 isok(k) = ispal(k*prime(k)) \\ _Alexandru Petrescu_, Feb 22 2023
%o A084122 (Python)
%o A084122 from sympy import sieve
%o A084122 def ok(n): return n and (s := str(n*sieve[n])) ==  s[::-1]
%o A084122 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Feb 22 2023
%Y A084122 Cf. A002113, A033286, A084121, A084123.
%K A084122 base,nonn,more
%O A084122 1,2
%A A084122 _Giovanni Resta_, May 14 2003