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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

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OFFSET

1,1

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.

LINKS

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

EXAMPLE

a(1) = 2 = 1 * 1 + 1.

a(3) = 11 = 10 * 1 + 1.

a(13) = 977 = 16 * 61 + 1.

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);