A286630 -id:A286630 - cp's OEIS frontend

A276155 Complement of A276154; numbers that cannot be obtained by shifting left the primorial base representation (A049345) of some number.

1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 64, 65, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 93, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 108, 109

Offset: 1

Antti Karttunen, Aug 24 2016

The first 25 terms, when viewed in primorial base (A049345) look as: 1, 11, 20, 21, 101, 111, 120, 121, 201, 211, 220, 221, 300, 301, 310, 311, 320, 321, 400, 401, 410, 411, 420, 421, 1001.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to primorial base

Complement: A276154.
Row 1 of A276943 and A286623. Column 1 of A276945 and A286625.
Cf. A002110, A049345.
Cf. A005408, A057588, A061720, A143293, A286630 (subsequences).
For the first 17 terms coincides with A273670.

nn = 109; b = MixedRadix[Reverse@ Prime@ NestWhileList[# + 1 &, 1, Times @@ Prime@ Range[# + 1] <= nn &]]; Complement[Range@ nn, Table[FromDigits[#, b] &@ Append[IntegerDigits[n, b], 0], {n, 0, nn}]] (* Version 10.2, or *)
nn = 109; f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], Times @@ Prime@ Range[# - i]]], {i, 0, #}] &@ NestWhile[# + 1 &, 0, Times @@ Prime@ Range[# + 1] <= n &]; Rest[a][[All, 1]]]; Complement[Range@ nn, Table[Total[Times @@@ Transpose@ {Map[Times @@ # &, Prime@ Range@ Range[0, Length@ # - 1]], Reverse@ #}] &@ Append[f@ n, 0], {n, 0, nn}]] (* Michael De Vlieger, Aug 26 2016 *)

A286629 a(n) = (A000040(n)-1) * A002110(n).

Original entry on oeis.org

2, 12, 120, 1260, 23100, 360360, 8168160, 174594420, 4908043140, 181151410440, 6016814703900, 267146572853160, 12170010541088400, 549475975930141260, 28284929999070604860, 1694636240813882325960, 111520100308944333066060, 7037302881564418258996200, 518649222371297625688019940, 39055858108868927267719077300

Offset: 1

Antti Karttunen, Jul 07 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..120
Index entries for sequences related to primorial base

Cf. A000040, A002110, A006093, A061720, A276154, A286630.

Table[(Prime[n] - 1) Product[Prime[k], {k, n}], {n, 100}] (* Indranil Ghosh, Jul 07 2017 *)

a(n) = (prime(n)-1)*prod(k=1, n, prime(k)); \\ Michel Marcus, Jul 07 2017

from sympy import prime, primorial
def a002110(n): return 1 if n<1 else primorial(n)
def a(n): return (prime(n) - 1)*a002110(n)
print([a(n) for n in range(1, 21)]) # Indranil Ghosh, Jul 07 2017

(define (A286629 n) (* (- (A000040 n) 1) (A002110 n)))

a(n) = A006093(n) * A002110(n) = (A000040(n)-1) * A002110(n).
a(n) = A286630(n) - A002110(n).
a(n) = A276154(A061720(n-1)).

cp's OEIS Frontend

A276155 Complement of A276154; numbers that cannot be obtained by shifting left the primorial base representation (A049345) of some number.

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A286629 a(n) = (A000040(n)-1) * A002110(n).

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