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 A023087 Numbers k such that k and 3*k are anagrams. 11
 0, 1035, 2475, 10035, 10350, 12375, 14247, 14724, 23751, 24147, 24714, 24750, 24876, 24975, 27585, 28575, 100035, 100350, 102375, 103428, 103500, 107235, 113724, 114237, 123507, 123714, 123750, 123876, 123975, 124137, 128034, 134505, 135045 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All terms are divisible by 9. - Eric M. Schmidt, Jul 12 2014 From Petros Hadjicostas, Jul 28 2020: (Start) 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. 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. 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. 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) REFERENCES Fred Schuh, The Master Book of Mathematical Recreations, Dover, New York, 1968, pp. 25-31. LINKS Zak Seidov and David W. Wilson, Table of n, a(n) for n = 1..10001 (first 3000 terms from Zak Seidov) MATHEMATICA 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 *) CROSSREFS Cf. A023086, A023088, A023089, A023090, A023091, A023092, A023093, A336661. Sequence in context: A245680 A241787 A175692 * A219445 A163558 A025412 Adjacent sequences: A023084 A023085 A023086 * A023088 A023089 A023090 KEYWORD nonn,base AUTHOR STATUS approved

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)