cp's OEIS Frontend

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.

A023087 Numbers k such that k and 3*k are anagrams.

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%I A023087 #40 Jul 29 2020 02:58:14
%S A023087 0,1035,2475,10035,10350,12375,14247,14724,23751,24147,24714,24750,
%T A023087 24876,24975,27585,28575,100035,100350,102375,103428,103500,107235,
%U A023087 113724,114237,123507,123714,123750,123876,123975,124137,128034,134505,135045
%N A023087 Numbers k such that k and 3*k are anagrams.
%C A023087 All terms are divisible by 9. - _Eric M. Schmidt_, Jul 12 2014
%C A023087 From _Petros Hadjicostas_, Jul 28 2020: (Start)
%C A023087 This is Schuh's (1968) "treble puzzle" (the treble of k is 3*k). On five pages of his book, he finds the two 4-digit numbers that belong to this sequence (1035 and 2475), the thirteen 5-digit numbers of the sequence and the 104 6-digit numbers of the sequence. Note that if m belongs to the sequence, so does 10*m.
%C A023087 All numbers in this sequence are permutations of numbers that are combinations of numbers from A336661, which is related to another puzzle of Schuh (1968). Before he solved this puzzle, he had to solve the puzzle described in A336661.
%C A023087 For example, 1035 is a permutation of the number 3015 which is a combination of the numbers 301 and 5 that appear in A336661. As another example, note that 12375 and 23751 are both permutations of 31725, which is formed by combining the numbers 31, 72 and 5 from sequence A336661.
%C A023087 If we also admit zeros as initial digits, then we find more solutions to this sequence: 0351, 00351, 01035, 03501, 02475, ... These numbers are also permutations of numbers that can be formed by combining numbers in A336661. (End)
%D A023087 Fred Schuh, The Master Book of Mathematical Recreations, Dover, New York, 1968, pp. 25-31.
%H A023087 Zak Seidov and David W. Wilson, <a href="/A023087/b023087.txt">Table of n, a(n) for n = 1..10001</a> (first 3000 terms from Zak Seidov)
%t A023087 si[n_] := Sort@ IntegerDigits@ n; Flatten@ {0, Table[ Select[ Range[10^d + 8, 4 10^d - 1, 9], si[#] == si[3 #] &], {d, 0, 6}]} (* _Giovanni Resta_, Mar 20 2017, corrected by _Philippe Guglielmetti_, Jul 16 2018 *)
%Y A023087 Cf. A023086, A023088, A023089, A023090, A023091, A023092, A023093, A336661.
%K A023087 nonn,base
%O A023087 1,2
%A A023087 _David W. Wilson_