A339543 Beginnings of record-length chains of primes under iteration of A339541.

1, 2, 1483, 2239, 3023417

Offset

1,2

Comments

A number n is in this sequence if the sequence defined by x(k+1) = A339541(k) with x(0)=n has more initial primes than the sequences for smaller n.

No more terms < 10^8.

Links

Table of n, a(n) for n=1..5.

Example

Starting with 1483 we get A339541(1483) = 1511, A339541(1511) = 1531, A339541(1531) = 1541, A339541(1541) = 1552.  This makes 4 initial primes (1483, 1511, 1531, 1541 but not 1552), which is more than we get starting with any number < 1483, so 1483 is in the sequence.

Maple

sod:= (n.b) -> convert(convert(n, base, b), `+`):
f:= n -> n + sod(n, sod(n, 10)):
g:= proc(n) option remember;
if isprime(n) then 1 + procname(f(n))
else 0
fi
end proc:
R:= 1: vmax:= 0: p:= 1:
while p < 10^7 do
  p:= nextprime(p);
  v:= g(p);
  if v > vmax then
   R:= R, p; vmax:= v;
  fi
od:
R;

Crossrefs

Cf. A339541, A339542.

Sequence in context: A259323 A172939 A172234 * A023291 A319329 A058423

Adjacent sequences: A339540 A339541 A339542 * A339544 A339545 A339546

Keyword

nonn,base,bref,more

Author

J. M. Bergot and Robert Israel, Dec 08 2020

Status

approved