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

1,1

Links

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

Formula

A317241(a(n)) = 0.

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 *)

Crossrefs

Column k=0 of A317390.

Cf. A180337 (subsequence), A317241.

Sequence in context: A006066 A084935 A239072 * A217302 A062409 A342939

Adjacent sequences: A317239 A317240 A317241 * A317243 A317244 A317245

Keyword

nonn

Author

Alois P. Heinz, Jul 24 2018

Status

approved