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

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

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

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)

Crossrefs

Cf. A023086, A023088, A023089, A023090, A023091, A023092, A023093, A336661.

Programs

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 *)