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 A317422 a(n) is the smallest positive integer such that with the letters of the name of that number we can spell the name of exactly n smaller positive integers. 2
 15, 13, 14, 21, 24, 72, 76, 74, 113, 115, 121, 171, 122, 150, 131, 142, 127, 147, 124, 129, 159, 138, 135, 153, 137, 156, 126, 125, 128, 165, 168, 157, 158, 467, 289, 265, 267, 487, 275, 392, 278, 754, 692, 492, 257, 857, 572, 524, 674, 428, 1133, 748, 1322, 867 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(2065) > 100000. - Hans Havermann, Aug 10 2018 REFERENCES Sequence Fans Mailing list. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..2064 from Hans Havermann, terms 1..100 from Daniel Suteu) EXAMPLE a(1) = 15 because with the letters of 'fifteen' we can write only one smaller number: ten. And 15 is the smallest number for which this is so. (We cannot write 'nine' because that requires two letters 'n'.) a(10) = 115 because with the letters of 'one hundred fifteen' we can write the name of ten smaller numbers: one, three, four, nine, ten, fourteen, fifteen, nineteen, one hundred, one hundred ten. PROG (Python) from num2words import num2words as n2w from collections import Counter from itertools import count, islice def key(n): return Counter(c for c in n2w(n).replace(" and", "") if c.isalpha()) def included(c1, c2): # in Python 3.10+, use c[i] <= c[k] in agen() return all(c1[c] <= c2[c] for c in c1) def agen(): n, adict, c = 1, {0: 1}, [None] for k in count(1): c.append(key(k)) v = sum(1 for i in range(1, k) if included(c[i], c[k])) if v not in adict: adict[v] = k while n in adict: yield adict[n]; n += 1 if k%10000 == 0: print("...", k) print(list(islice(agen(), 54))) # Michael S. Branicky, Aug 19 2022 CROSSREFS Cf. A317423 (Spanish). Sequence in context: A195533 A299315 A072348 * A129786 A104056 A131285 Adjacent sequences: A317419 A317420 A317421 * A317423 A317424 A317425 KEYWORD nonn,word AUTHOR Claudio Meller, Jul 27 2018 STATUS approved

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Last modified December 1 18:36 EST 2023. Contains 367500 sequences. (Running on oeis4.)