

A276155


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


8



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
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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 IntSeqlibrary)
(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



