A345407 a(n) is the first semiprime that starts a sequence of n distinct semiprimes under the map A001414.

4, 9, 14, 33, 62, 177, 886, 2649, 5294, 68653, 496966, 1490889, 16896262

Offset

1,1

Comments

a(14) >= 10^8. - Martin Ehrenstein, Jan 31 2022

Links

Table of n, a(n) for n=1..13.

C. Rivera, Puzzle 1074 Semiprimes stairs, The prime puzzles and problems connection, Feb. 2022

Example

a(1) = 4 which is a semiprime (note 2*2 = 2+2, which is why the word "distinct" is in the Name).
a(3) = 14 = 2*7 -> 9 (semiprime) = 3*3 -> 3+3 = 6 (semiprime) = 2*3 -> 2+3 = 5 (not semiprime).

Maple

f:= proc(n) local L, a, b; option remember;
    L:= ifactors(n)[2];
    if nops(L) = 1 and L[1][2] = 2 then
       1 + procname(2*L[1][1])
    elif nops(L) = 2 and L[1][2]+L[2][2]=2 then
       1 + procname(L[1][1]+L[2][1])
    else 0
    fi
end proc:
f(4):= 1:
V:= map(f, [$1..10^6]):
W:= Vector(11):
for nn from 1 to 10^6 do
  if V[nn] > 0 and W[V[nn]] = 0 then W[V[nn]]:= nn fi
od:
convert(W, list);

Crossrefs

Cf. A001358, A001414.

Sequence in context: A086192 A105503 A095169 * A105703 A055453 A247013

Adjacent sequences: A345404 A345405 A345406 * A345408 A345409 A345410

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Jan 27 2022

Extensions

a(13) from Martin Ehrenstein, Jan 31 2022

Status

approved