A008537 - OEIS

%I #31 Aug 08 2023 18:00:53

%S 0,2,3,4,5,6,8,12,30,32,33,34,35,36,38,40,42,43,44,45,46,48,50,52,53,

%T 54,55,56,58,60,62,63,64,65,66,68,80,82,83,84,85,86,88

%N Numbers that do not contain the letter 'n'.

%C From _M. F. Hasler_, Apr 01 2019: (Start)

%C This sequence contains 42 nonzero terms below 10^9, plus the initial a(1) = 0.

%C Since "hundred", "thousand", "million" etc. are forbidden, the only way to extend the sequence would be to use long scale with "milliard" for 10^9: then the next term would be a(44) = 2*10^9 = "two milliards", a(45) = 2*10^9 + 2, and so on.

%C The 2019 "April Fools contest" on codeforces.com referred to these numbers as "Kanban numbers", i.e., numbers which ban the letters 'k', 'a' and 'n'. But no 'k' ever appears, and unless we consider "milliard", 'a' only appears (in "thousand" and later "quadrillion") in conjunction with 'n', which therefore is the only relevant. So "n-ban (or maybe: anban) numbers" would be more a adequate name. (End)

%H GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See Puzzle 114, p. 56.

%H Mariia Mykhailova (alias Nickolas), <a href="https://codeforces.com/contest/1145/problem/B">April Fools Day Contest 2019 - B: Kanban Numbers</a>, on codeforces.com, April 1, 2019.

%o (PARI) is(n)=!setsearch(Set(Vec(English(n))),"n") \\ See A052360 for English(). - _M. F. Hasler_, Apr 01 2019

%o (Python)

%o from num2words import num2words

%o afull = [k for k in range(100) if "n" not in num2words(k)]

%o print(afull) # _Michael S. Branicky_, Aug 18 2022

%Y Cf. A006933 (eban numbers: without 'e'), A089589 (without 'i'), A008521 (without 'o'), A089590 (without 'u'), A008523 (without 't'), A072956 (turban numbers: without r, t or u), A072957 (urban numbers: without r or u).

%K nonn,word,fini,full

%O 1,2

%A _N. J. A. Sloane_

%E Edited by _M. F. Hasler_, Apr 01 2019