A344032 a(n) is the least prime that begins a sequence of at least n distinct primes under iteration of A061762.

2, 11, 23, 53, 12451, 36779999

Offset: 1

Author

J. M. Bergot and Robert Israel, May 07 2021

Keywords

• nonn
• base
• more

Examples

			12451 is prime and A061762(12451) = 1*2*4*5*1+1+2+4+5+1 = 53.
53 is prime and A061762(53) = 5*3+5+3 = 23.
23 is prime and A061762(23) = 2*3+2+3 = 11.
11 is prime and A061762(11) = 1*1+1+1 = 3.
3 is prime and A061762(3) = 3+3 = 6 is not prime.
Thus 12451 begins a sequence of 5 distinct primes under the iteration of A061762.  Since 12451 is the least such prime, a(5) = 12451.
		

Crossrefs

Cf. A061762, A214629.

Programs

Maple

f:= proc(n) local L;
   L:= convert(n,base,10);
   convert(L,`+`)+convert(L,`*`)
end proc:
g:= proc(n) local S,v;
  S:= {n}:
  v:= n;
  do
    v:= f(v);
    if member(v,S) or not isprime(v) then return nops(S) fi;
    S:= S union {v}
  od
end proc:
R:= NULL: p:= 1: m:= 0:
while m < 5 do
  p:= nextprime(p);
  v:= g(p);
  if v > m then R:= R, p$(v-m); m:= v fi
od:
R;