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A372197 Primes that can be represented as k*R(k) + 1, where R(k) is the reverse of k.

%I A372197 #15 Jul 07 2024 21:03:41
%S A372197 2,5,11,17,37,41,101,251,401,491,641,811,977,1009,1301,1459,1601,1613,
%T A372197 2269,2297,2521,4001,4357,4931,5741,5849,8101,9001,10891,12071,12101,
%U A372197 13001,14621,16001,17291,19441,22961,23633,26681,27011,30493,31541,34781,38153,42283,42751,46061,58481,66457
%N A372197 Primes that can be represented as k*R(k) + 1, where R(k) is the reverse of k.
%C A372197 Values of the primes corresponding to A073805, sorted and with duplicates removed.
%C A372197 Most terms can be obtained in two ways, corresponding to x * R(x) + 1 and R(x) * x + 1 or more generally (10^i * x) * R(x) + 1 and (10^i * R(x)) * x + 1, where R(x) <> x and x doesn't end in 0 so R(R(x)) = x.  The first term that can be obtained in four ways is 1015561 = 1560 * 651 + 1 = 2730 * 372 + 1 = 3720 * 273 + 1 = 6510 * 156 + 1.
%H A372197 Robert Israel, <a href="/A372197/b372197.txt">Table of n, a(n) for n = 1..10000</a>
%e A372197 a(1) = 2 = 1 * 1 + 1.
%e A372197 a(3) = 11 = 10 * 1 + 1.
%e A372197 a(13) = 977 = 16 * 61 + 1.
%p A372197 N:= 6: # for terms <= 10^N where N is even
%p A372197 S:= {}:
%p A372197 for x from 1 to 10^(N/2)-1 do
%p A372197   if x mod 10 = 0 then next fi;
%p A372197   r:= rev(x);
%p A372197   if r < x then next fi;
%p A372197   v:= x*r;
%p A372197   for i from 0 do
%p A372197     w:= 10^i*v+1;
%p A372197     if w > 10^N then break fi;
%p A372197     if isprime(w) then S:= S union {w} fi;
%p A372197   od
%p A372197 od:
%p A372197 sort(convert(S,list));
%Y A372197 Cf. A004086, A073805.
%K A372197 nonn,base
%O A372197 1,1
%A A372197 _Robert Israel_, Jul 03 2024