This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A336661 #46 Jul 30 2020 04:03:59 %S A336661 0,4,5,9,31,72,86,301,431,602,715,842,856,973,986,4301,6015,7142,7302, %T A336661 7315,8426,8572,8602,9713,9726,9843,9856,60142,71302,73015,73142, %U A336661 84302,85602,85726,97143,97156,97286,98426,98573,714302,715602,726015,730142,843026,843156,857142,857302,860142,971426,972843,972856,973026,973156,984273,985713,985726,986013 %N A336661 Numbers that have decimal expansion c(1)c(2)...c(n) with distinct digits that satisfy c(1) <> 0, c(1) is the largest digit, and for each i in 1..n there is j in 0..2 such that c(i) == 3*c(i-1) + j (mod 10) (with c(0): = c(n)). %C A336661 This is one of Schuh's examples of a puzzle tree. %C A336661 Putting the number on a circle and going clockwise, we observe that a 0 is followed by a 1 or 2; a 1 is followed by a 3, 4, or 5; a 2 is followed by a 6, 7, or 8; a 3 is followed by a 0, 1, or 9; a 4 is followed by a 2 or 3; a 5 is followed by a 6 or 7; a 6 is followed by a 0, 8, or 9; a 7 is followed by a 1, 2, or 3; an 8 is followed by a 4, 5, or 6; and a 9 is followed by a 7 or 8. (These observations assume the number has at least two digits.) %C A336661 Schuh (pp. 25-31) uses the solution to this problem to solve the "trebles puzzle": find all numbers (with no initial 0) that are written with the same digits as their treble (the treble of k is 3*k). These numbers are listed in A023087. %C A336661 The number 0 has been included here for two reasons: (i) we may assume that it satisfies the conditions of the problem vacuously, and (ii) its inclusion allows Schuh to solve the "treble puzzle". The numbers in A023087 are all permutations of combinations of numbers in this sequence. %D A336661 Fred Schuh, The Master Book of Mathematical Recreations, Dover, New York, 1968, pp. 8-10. %H A336661 Petros Hadjicostas, <a href="/A336661/b336661.txt">Table of n, a(n) for n = 1..141</a> %H A336661 David A. Corneth, <a href="/A336661/a336661.gp.txt">PARI program</a>. [It generates all 141 terms of this finite sequence.] %H A336661 Wikipedia, <a href="https://en.wikipedia.org/wiki/Frederik_Schuh">Frederik Schuh</a>. %H A336661 Dutch Wikipedia, <a href="https://nl.wikipedia.org/wiki/Frederik_Schuh">Frederik Schuh</a>. [Has more extensive biography in Dutch.] %e A336661 In all the cases below, the first digit must be the largest and all the digits must be distinct. %e A336661 4 belongs to this list because c(1) = 4 = c(0) and 4 == 3*4 + 2 (mod 10). %e A336661 31 belongs to this list because c(1) = 3, c(2) = 1 = c(0), 3 == 3*1 (mod 10), and 1 == 3*3 + 2 (mod 10). %e A336661 301 belongs to this list because 3 == 3*1 (mod 10), 0 == 3*3 + 1 (mod 10), and 1 == 3*0 + 1 (mod 10). %e A336661 4301 belongs to this list because 4 == 3*1 + 1 (mod 10), 3 == 3*4 + 1 (mod 10), 0 == 3*3 + 1 (mod 10), and 1 == 3*0 + 1 (mod 10). %e A336661 60142 belongs to this list because 6 == 3*2 (mod 10), 0 == 3*6 + 2 (mod 10), 1 == 3*0 + 1 (mod 10), 4 = 3*1 + 1 (mod 10), and 2 = 3*4 (mod 10). %o A336661 (PARI) See Corneth link %Y A336661 Cf. A023087. %K A336661 nonn,base,fini %O A336661 1,2 %A A336661 _Petros Hadjicostas_, Jul 28 2020