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A372197
Primes that can be represented as k*R(k) + 1, where R(k) is the reverse of k.
1
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
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
Sequence in context: A059987 A027426 A133928 * A126204 A091936 A153145
KEYWORD
nonn,base
AUTHOR
Robert Israel, Jul 03 2024
STATUS
approved