A130604 Numbers whose base-10 and base-7 representations are permutations of the same multiset of digits.

0, 1, 2, 3, 4, 5, 6, 23, 46, 265, 316, 1030, 1234, 1366, 1431, 1454, 2060, 2116, 10144, 10342, 10542, 11425, 12415, 12450, 12564, 12651, 13045, 13245, 13534, 14610, 15226, 15643, 16255, 16546, 16633, 101046, 101264, 102615, 103260, 103316, 103460, 103461, 103462, 103463, 103464, 103465, 103466, 104126, 104632, 104650, 104651, 104652, 104653, 104654, 104655, 104656, 105266, 106235, 106253, 113256, 116336

Offset: 1

Author

Paul Lusch, Aug 10 2007

Keywords

• nonn
• base
• fini
• full

Comments

The sequence is finite and full since any d-digit number is < 7^d in base 7 and > 10^(d-1) in base 10. But 1000000 = 10^6 > 7^7 = 823543, so any term must have 6 or fewer digits and all those are present. - Michael S. Branicky, Apr 22 2023

Examples

			14610 is represented as 14610 in base 10 and as 60411 in base 7. Each representation is a permutation of the multiset {0,1,1,4,6}.
		

Crossrefs

Cf. A037440, A074233.

Programs

Mathematica

Select[Range[10,110000],Sort[IntegerDigits[#]]==Sort[IntegerDigits[#,7]]&] (* Harvey P. Dale, Sep 23 2017 *)

Python

from sympy.ntheory import digits
def ok(n): return sorted(map(int, str(n))) == sorted(digits(n, 7)[1:])
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Apr 22 2023

Extensions

a(1)-a(7) inserted and a(43)-a(61) from Michael S. Branicky, Apr 22 2023