A317242 Positive integers having no representation of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

2, 5, 7, 11, 15, 23, 26, 27, 28, 31, 33, 35, 36, 47, 50, 56, 57, 63, 66, 78, 81, 82, 95, 96, 106, 116, 119, 120, 122, 129, 136, 156, 162, 166, 167, 190, 193, 215, 218, 219, 227, 236, 244, 254, 263, 286, 289, 330, 335, 342, 352, 359, 387, 393, 395, 396, 414

Offset: 1

Author

Alois P. Heinz, Jul 24 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Column k=0 of A317390.

Cf. A180337 (subsequence), A317241.

Programs

Maple

q:= proc(n, s) option remember; is (n=1 or ormap(p->
      q((n-1)/p, s union {p}), numtheory[factorset](n-1) minus s))
    end:
a:= proc(n) option remember; local k; for k from
     `if`(n=1, 2, 1+a(n-1)) while q(k, {}) do od; k
    end:
seq(a(n), n=1..100);

Mathematica

b[n_, s_] := b[n, s] = If[n == 1, 1, Sum[If[p == 1, 0, b[(n - 1)/p, s ~Union~ {p}]], {p, FactorInteger[n - 1][[All, 1]] ~Complement~ s}]];
Position[Array[b[#, {}]&, 10^5], 0] // Flatten (* Jean-François Alcover, Jul 14 2021, after Alois P. Heinz in A317241 *)

Formula

A317241(a(n)) = 0.