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

2, 5, 11, 17, 37, 41, 101, 251, 401, 491, 641, 811, 977, 1009, 1301, 1459, 1601, 1613, 2269, 2297, 2521, 4001, 4357, 4931, 5741, 5849, 8101, 9001, 10891, 12071, 12101, 13001, 14621, 16001, 17291, 19441, 22961, 23633, 26681, 27011, 30493, 31541, 34781, 38153, 42283, 42751, 46061, 58481, 66457

Offset: 1

Author

Robert Israel, Jul 03 2024

Keywords

• nonn
• base

Comments

Values of the primes corresponding to A073805, sorted and with duplicates removed.

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.

Examples

			a(1) = 2 = 1 * 1 + 1.
a(3) = 11 = 10 * 1 + 1.
a(13) = 977 = 16 * 61 + 1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004086, A073805.

Programs

Maple

N:= 6: # for terms <= 10^N where N is even
S:= {}:
for x from 1 to 10^(N/2)-1 do
  if x mod 10 = 0 then next fi;
  r:= rev(x);
  if r < x then next fi;
  v:= x*r;
  for i from 0 do
    w:= 10^i*v+1;
    if w > 10^N then break fi;
    if isprime(w) then S:= S union {w} fi;
  od
od:
sort(convert(S,list));