OFFSET
1,2
COMMENTS
Numbers k such that, if p is the least prime such that the digit reversal of k * p is prime, for every j < k either there is a prime q < p such that the digit reversal of j * q is prime or there is no prime q such that the digit reversal of j * q is prime.
A373779(10^k + 1) > 10^k for even k, so 10^k + 1 is likely to be a term.
Similarly, A373779(2 * 10^k + 2) >= 1.5 * 10^k - 1 for even k > 2.
a(13) > 10^7.
EXAMPLE
a(3) = 23 is a term because 17 and reverse(23 * 17) = 193 are prime, there is no prime p < 17 for which reverse(23 * p) is prime, and for every j < 23 there is either no prime p with reverse(j * p) prime or there is such a p < 17.
MAPLE
rev:= proc(n) local L, i;
L:= convert(n, base, 10);
add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
f:= proc(n) local p;
if n mod 3 = 0 or n mod 11 = 0 then return -1 fi;
p:= 1;
do
p:= nextprime(p);
if isprime(rev(n*p)) then return p fi
od;
end proc:
R:= 1: m:= 2: count:= 1:
for i from 2 while count < 12 do
v:= f(i);
if v > m then
count:= count+1; R:= R, i; m:= v;
fi
od:
R;
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Robert Israel, Jun 18 2024
EXTENSIONS
a(13)-a(14) from Michael S. Branicky, Jun 24 2024
STATUS
approved