A345217 a(n) is the first emirp that starts a chain of exactly n emirps under the mapping f(x) = x + reverse(x) + 1.

13, 149, 70949, 12314597

Offset

1,1

Comments

a(n) == 5 (mod 6) for n >= 2.

No more terms < 16*10^11. - Lars Blomberg, Jun 25 2021

Links

Table of n, a(n) for n=1..4.

Example

a(1) = 13 is the first emirp, but 13+31+1 = 45 is not an emirp.
a(2) = 149 because 149 and 149+941+1 = 1091 are emirps, but 1091+1901+1 = 2993 is not an emirp.
a(3) = 70949 because 70949, 70949+94907+1 = 165857, and 165857+758561 = 924419 are emirps, but 924419+914429+1 = 1838849 is not an emirp.

Maple

revdigs:= 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 r, t, x;
  x:= n;
  for t from 0 do
    if not isprime(x) then return t fi;
    r:= revdigs(x);
    if not (r <> n and isprime(x) and isprime(r)) then return t fi;
    x:= x+r+1;
  od;
end proc:
V:= Vector(4): V[1]:= 13: count:= 1:
for n from 17 by 6 while count < 4 do
  v:= f(n);
  if v > 0 and V[v] = 0 then V[v]:= n; count:= count+1 fi;
od:
convert(V, list);

Crossrefs

Cf. A006567.

Sequence in context: A125448 A163148 A355414 * A185405 A051475 A242576

Adjacent sequences: A345214 A345215 A345216 * A345218 A345219 A345220

Keyword

nonn,base,more

Author

J. M. Bergot and Robert Israel, Jun 10 2021

Status

approved