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

1,2

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base

Mathematica

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A276155 (COMPLEMENT 1 A276154))

Crossrefs

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.

Sequence in context: A275319 A285343 A335002 * A273670 A153329 A213637

Adjacent sequences: A276152 A276153 A276154 * A276156 A276157 A276158

Keyword

nonn,base

Author

Antti Karttunen, Aug 24 2016

Status

approved