A072957 - OEIS

%I #14 Aug 19 2022 13:52:34

%S 1,2,5,6,7,8,9,10,11,12,15,16,17,18,19,20,21,22,25,26,27,28,29,50,51,

%T 52,55,56,57,58,59,60,61,62,65,66,67,68,69,70,71,72,75,76,77,78,79,80,

%U 81,82,85,86,87,88,89,90,91,92,95,96,97,98,99,1000000,1000001,1000002

%N Urban numbers: without 'r' or 'u'.

%D M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002).

%H Michael S. Branicky, <a href="/A072957/b072957.txt">Table of n, a(n) for n = 1..10000</a>

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

%o /* Alternate code, not using English(): (valid for 1 <= n < one trillion, which should be forbidden due to the 'r' but returns 1) */

%o is(n)={setintersect( Set(digits(n)), [3,4]) && return; !while(n=divrem(n,10^6), n[2]<100||return; n=n[1])} \\ _M. F. Hasler_, Apr 01 2019

%o (Python)

%o from num2words import num2words

%o from itertools import islice, product

%o def ok(n): return set(num2words(n)) & {"r", "u"} == set()

%o def agen(): # generator of terms < 10**304

%o     base, pows = [k for k in range(1, 1000) if ok(k)], [1]

%o     yield from ([0] if ok(0) else []) + base

%o     for e in range(3, 304, 3):

%o         if set(num2words(10**e)[4:]) & {"r", "u"} == set():

%o             pows = [10**e] + pows

%o             for t in product([0] + base, repeat=len(pows)):

%o                 if t[0] == 0: continue

%o                 yield sum(t[i]*pows[i] for i in range(len(t)))

%o print(list(islice(agen(), 66))) # _Michael S. Branicky_, Aug 19 2022

%Y Cf. A006933 (eban numbers: without 'e'), A008521 (without 'o'), A008523 (without 't'), A008537 (without 'n'), A089590 (without 'u'), A072956 (turban numbers: without r, t or u), A089589 (without 'i').

%K easy,nonn,word

%O 1,2

%A _Michael Joseph Halm_, Aug 13 2002

%E Missing term 52 inserted by _Michael S. Branicky_, Aug 19 2022