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 A370402 Lexicographically earliest sequence of distinct nonnegative terms such that the last digit of a(n) is present in a(n+1) and the last letter of the English name of a(n) is present in the English name of a(n+1). 6
 0, 40, 20, 30, 50, 60, 70, 80, 90, 120, 130, 140, 150, 160, 170, 180, 190, 220, 230, 240, 250, 260, 270, 280, 290, 320, 330, 340, 350, 360, 370, 380, 390, 420, 430, 440, 450, 460, 470, 480, 490, 520, 530, 540, 550, 560, 570, 580, 590, 620, 630, 640, 650, 660, 670, 680, 690, 720, 730, 740, 750, 760, 770, 780 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS When will the first integer not ending in zero appear? Answer: a(83) = 1021. - Michael S. Branicky, Feb 18 2024 LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 Eric Angelini, Talking to me?, personal blog, Feb 2024. EXAMPLE 0 zero, 40 forty, 20 twenty, 30 thirty, 50 fifty, 60 sixty, 70 seventy, 80 eighty, 90 ninety, 120 one hundred twenty, 130 one hundred thirty, 140 one hundred forty, 150 one hundred fifty, 160 one hundred sixty, 170 one hundred seventy, etc. MATHEMATICA a[1]=0; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]|| FreeQ[IntegerDigits@k, Mod[a[n-1], 10]]|| !StringContainsQ[IntegerName[k, "Words"], Last@Characters@IntegerName[a[n-1], "Words"]], k++]; k); Array[a, 64] PROG (Python) from num2words import num2words from itertools import count, islice def name(n): return num2words(n).replace(" and", "") def agen(): # generator of terms an, aset, mink = 0, set(), 1 while True: yield an aset.add(an) t1, t2, k = str(an%10), name(an)[-1], mink an = next(k for k in count(mink) if k not in aset and t1 in str(k) and t2 in name(k)) while mink in aset: mink += 1 print(list(islice(agen(), 64))) # Michael S. Branicky, Feb 18 2024 CROSSREFS Cf. A370400, A370401, A370403, A370404, A370405. Sequence in context: A365051 A033975 A033360 * A029543 A097208 A216137 Adjacent sequences: A370399 A370400 A370401 * A370403 A370404 A370405 KEYWORD base,nonn,word AUTHOR Eric Angelini and Giorgos Kalogeropoulos, Feb 17 2024 STATUS approved

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Last modified September 9 06:59 EDT 2024. Contains 375762 sequences. (Running on oeis4.)