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 A135600 Angled numbers with an internal digit as the vertex. 9
 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The structure of digits represents an angle. The vertex is an internal digit. In the graphic representation the points are connected by imaginary line segments from left to right. The last acute-angled number of this sequence has 14 digits: 98765432102468. The last right-angled number of this sequence has 19 digits: 9876543210123456789. All 3-digit numbers are terms of this sequence. Next terms are 1000, 1012, 1024, 1036, 1048, 1110, 1111, 1112, 1113, 1114, .... For each k >= 20, there are 363 k-digit terms: 354 obtuse-angled and 9 straight-angled.- Michael S. Branicky, Aug 03 2022 LINKS David A. Corneth, Table of n, a(n) for n = 1..10910 David A. Corneth, PARI program EXAMPLE The acute-angled number 12342 (see A135601): . . . . . . . . 4 . . . 3 . . . 2 . . 2 1 . . . . The right-angled number 12343 (see A135602): . . . . . . . . 4 . . . 3 . 3 . 2 . . . 1 . . . . The obtuse-angled number 12344 (see A135603): . . . . . . . . 4 4 . . 3 . . . 2 . . . 1 . . . . The straight-angled (or straight-line) number 12345 (see A135643): . . . . 5 . . . 4 . . . 3 . . . 2 . . . 1 . . . . PROG (PARI) See PARI link \\ David A. Corneth, Aug 02 2022 (Python) from itertools import count, islice def agen(): seeds = [k for k in range(100, 1000)] for digits in count(4): yield from sorted(seeds) new, pow10 = set(), 10**(digits-1) for q in seeds: d = list(map(int, str(q))) e1, e2 = d[0] - (d[1]-d[0]), d[-1] + (d[-1]-d[-2]) if 9 >= e1 > 0: new.add(e1*pow10 + q) if 9 >= e2 >= 0: new.add(10*q + e2) seeds = new print(list(islice(agen(), 50))) # Michael S. Branicky, Aug 03 2022 CROSSREFS Cf. A134810, A134853, A134941, A134970, A135641, A135642, A135643, A135601, A135602, A135603. Sequence in context: A115048 A112525 A000865 * A134999 A301516 A204581 Adjacent sequences: A135597 A135598 A135599 * A135601 A135602 A135603 KEYWORD nonn,easy,base AUTHOR Omar E. Pol, Dec 02 2007 STATUS approved

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Last modified June 23 18:37 EDT 2024. Contains 373653 sequences. (Running on oeis4.)