A073417 Flawless numbers: numbers without a, f, l or w.

0, 1, 3, 6, 7, 8, 9, 10, 13, 16, 17, 18, 19, 30, 31, 33, 36, 37, 38, 39, 60, 61, 63, 66, 67, 68, 69, 70, 71, 73, 76, 77, 78, 79, 80, 81, 83, 86, 87, 88, 89, 90, 91, 93, 96, 97, 98, 99, 100, 101, 103, 106, 107, 108, 109, 110, 113, 116, 117, 118, 119, 130, 131, 133

Offset

1,3

Comments

1 and 6 seems to be the only numbers that are both flawless and perfect. 7 is the first odd number that is flawless but not perfect.

With the usual naming conventions, this is finite with a(336) = 999 the last term, due to thousAnd and -iLLion. - Michael S. Branicky, Jan 15 2026

References

Michael Joseph Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..336

Wikipedia, Names of Large Numbers

Example

6 is a term since its name SIX has no A, F, L or W.

Prog

(Python)
from num2words import num2words
from itertools import islice, product
def ok(n): return set(num2words(n).replace(" and", "")) & set("flaw") == set()
def afull(): return [k for k in range(1000) if ok(k)]
print(afull()) # Michael S. Branicky, Jan 15 2026

Crossrefs

Cf. A073416, A073418, A073419.

Sequence in context: A073850 A048748 A030781 * A299493 A047559 A288742

Adjacent sequences: A073414 A073415 A073416 * A073418 A073419 A073420

Keyword

easy,nonn,word,fini,full

Author

Michael Joseph Halm, Aug 23 2002

Extensions

Corrected by T. D. Noe, Nov 01 2006

Missing 60 inserted by Sean A. Irvine, Nov 28 2024

0 prepended by Michael S. Branicky, Jan 15 2026

Status

approved