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URL: https://oeis.org/A317242

⇱ A317242 - OEIS

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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.
4
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 24 2018
STATUS
approved