

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
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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 4digit numbers that belong to this sequence (1035 and 2475), the thirteen 5digit numbers of the sequence and the 104 6digit 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. 2531.


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

David W. Wilson


STATUS

approved



