A373780 Positions of records in A373779.

1, 2, 23, 31, 89, 101, 404, 3026, 10001, 20002, 1000001, 2000002, 100000001, 200000002

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.

Links

Table of n, a(n) for n=1..14.

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

Cf. A004086, A373779.

Sequence in context: A049568 A049556 A049580 * A061448 A007510 A117242

Adjacent sequences: A373777 A373778 A373779 * A373781 A373782 A373783

Keyword

nonn,base,more

Author

Robert Israel, Jun 18 2024

Extensions

a(13)-a(14) from Michael S. Branicky, Jun 24 2024

Status

approved