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

1,3

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

Links

Table of n, a(n) for n=1..61.

Example

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}.

Mathematica

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

Prog

(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

Crossrefs

Cf. A037440, A074233.

Sequence in context: A342999 A037404 A037440 * A359224 A262434 A246908

Adjacent sequences: A130601 A130602 A130603 * A130605 A130606 A130607

Keyword

nonn,base,fini,full

Author

Paul Lusch, Aug 10 2007

Extensions

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

Status

approved