A073416 Harmless numbers: numbers without a, h, m or r.

1, 2, 5, 6, 7, 9, 10, 11, 12, 15, 16, 17, 19, 20, 21, 22, 25, 26, 27, 29, 50, 51, 52, 55, 56, 57, 59, 60, 61, 62, 65, 66, 67, 69, 70, 71, 72, 75, 76, 77, 79, 90, 91, 92, 95, 96, 97, 99, 1000000000, 1000000001, 1000000002, 1000000005, 1000000006, 1000000007, 1000000009

Offset

1,2

Comments

There are significant overlaps with A039135 (numbers with same number of 3's and 4's) and A072957 (urban numbers without r or u).

References

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

Links

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

Example

5 is a term since its name FIVE has no A, H, M or R.

Prog

(Python)
from num2words import num2words
from itertools import islice, product
def ok(n): return set(num2words(n).replace(" and", "")) & set("harm") == 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:]) & set("harm") == 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(), 55))) # Michael S. Branicky, Jan 15 2026

Crossrefs

Cf. A039135, A072957.

Cf. A073417, A073418, A073419.

Sequence in context: A271107 A014355 A048972 * A188218 A050103 A303437

Adjacent sequences: A073413 A073414 A073415 * A073417 A073418 A073419

Keyword

easy,nonn,word

Author

Michael Joseph Halm, Aug 23 2002

Extensions

Numbers containing 8 (eight) removed by Sean A. Irvine, Nov 28 2024

a(52) onward from Michael S. Branicky, Jan 15 2026

Status

approved