A072957 Urban numbers: without 'r' or 'u'.

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, 52, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97, 98, 99, 1000000, 1000001, 1000002

Offset

1,2

References

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

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Prog

(PARI) is(n)=!setintersect(Set(Vec(English(n))), ["r", "u"]) \\ See A052360 for English(). - M. F. Hasler, Apr 01 2019
/* Alternate code, not using English(): (valid for 1 <= n < one trillion, which should be forbidden due to the 'r' but returns 1) */
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
(Python)
from num2words import num2words
from itertools import islice, product
def ok(n): return set(num2words(n)) & {"r", "u"} == set()
def agen(): # generator of terms < 10**304
    base, pows = [k for k in range(1, 1000) if ok(k)], [1]
    yield from ([0] if ok(0) else []) + base
    for e in range(3, 304, 3):
        if set(num2words(10**e)[4:]) & {"r", "u"} == set():
            pows = [10**e] + pows
            for t in product([0] + base, repeat=len(pows)):
                if t[0] == 0: continue
                yield sum(t[i]*pows[i] for i in range(len(t)))
print(list(islice(agen(), 66))) # Michael S. Branicky, Aug 19 2022

Crossrefs

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').

Sequence in context: A039239 A039182 A039135 * A073416 A138100 A039097

Adjacent sequences: A072954 A072955 A072956 * A072958 A072959 A072960

Keyword

easy,nonn,word

Author

Michael Joseph Halm, Aug 13 2002

Extensions

Missing term 52 inserted by Michael S. Branicky, Aug 19 2022

Status

approved