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

1,1

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);
  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));

Crossrefs

Cf. A004086, A073805.

Sequence in context: A059987 A027426 A133928 * A126204 A091936 A153145

Adjacent sequences: A372194 A372195 A372196 * A372198 A372199 A372200

Keyword

nonn,base

Author

Robert Israel, Jul 03 2024

Status

approved