A037440 -id:A037440 - cp's OEIS frontend

A308493 Numbers k such that k in base 10 contains the same digits as k in some other base.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 20, 21, 23, 31, 41, 42, 43, 46, 51, 53, 61, 62, 63, 71, 73, 81, 82, 83, 84, 86, 91, 93, 100, 101, 102, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 131, 133, 141, 144, 151, 155, 158, 161, 166, 171, 177, 181

Offset: 1

Jinyuan Wang, Aug 05 2019

Supersequence of A034294 and A307498.
This sequence is infinite because 2*10^k is a term for any k >= 0.
Also 10^k is a term when k >= 0 and so too 10^k*(10^m - 1)/9 for any k > 0 and m >= 0. - Bruno Berselli, Aug 26 2019

			k = 113 is in the sequence because the set of digits of k {1, 3} equals the set of digits of (k in base 110) = 13.

Cf. A034294, A037415, A037422, A037428, A037433, A037437, A037440, A037442, A037443, A249899, A307498.

isok(k) = {my(j=Set(digits(k))); for(b=2, k+1, if((b!=10) && (Set(digits(k, b)) == j), return(1))); return(0);} \\ Michel Marcus, Aug 05 2019

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

Original entry on oeis.org

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

Paul Lusch, Aug 10 2007

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

			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}.

Cf. A037440, A074233.

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

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

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

cp's OEIS Frontend

A308493 Numbers k such that k in base 10 contains the same digits as k in some other base.

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