A037404 -id:A037404 - cp's OEIS frontend

A037402 Numbers k such that every base-7 digit of k is a base-8 digit of k.

1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 57, 85, 94, 106, 114, 133, 142, 163, 171, 196, 204, 212, 220, 224, 225, 226, 227, 228, 229, 230, 236, 244, 277, 285, 305, 334, 342, 385, 392, 401, 540, 546, 547, 550, 597, 620, 629, 646, 688

Offset: 1

Clark Kimberling

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007093, A007094.

Cf. A037403, A037404.

import Data.List ((\\), nub)
a037402 n = a037402_list !! (n-1)
a037402_list = filter f [1..] where
   f x = null $ nub (ds 7 x) \\ nub (ds 8 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

b7b8Q[n_]:=Module[{idn7=Union[IntegerDigits[n,7]]},Intersection[ idn7, Union[ IntegerDigits[n,8]]]==idn7]; Select[Range[700],b7b8Q] (* Harvey P. Dale, Dec 15 2013 *)

A037403 Numbers k such that every base-7 digit of k is a base-9 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 31, 99, 106, 107, 195, 198, 248, 257, 284, 297, 321, 498, 514, 749, 750, 751, 758, 767, 785, 936, 939, 940, 943, 950, 968, 996, 1028, 1086, 1088, 1110, 1163, 1200, 1218, 1254, 1453, 1471, 1498, 1500, 1502, 1507

Offset: 1

Clark Kimberling

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007093, A007095.

Cf. A037402, A037404.

import Data.List ((\\), nub)
a037403 n = a037403_list !! (n-1)
a037403_list = filter f [1..] where
   f x = null $ nub (ds 7 x) \\ nub (ds 9 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

A037440 Positive numbers having the same set of digits in base 7 and base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 23, 46, 265, 316, 1030, 1234, 1336, 1366, 1401, 1431, 1443, 1454, 1464, 2060, 2116, 3261, 3515, 3621, 4631, 5052, 10144, 10342, 10542, 11134, 11425, 11524, 11544, 12415, 12450, 12532, 12564, 12651, 13035, 13045, 13245

Offset: 1

Clark Kimberling

			1336 is in the sequence because 1336 in base 7 is 3616.

John Cerkan, Table of n, a(n) for n = 1..10000

Subsequence of A037404.

Cf. A007093.

Select[Range@ 13300, Union@ IntegerDigits@ # == Union@ IntegerDigits[#, 7] &] (* Michael De Vlieger, Feb 18 2017 *)

isok(n) = Set(digits(n, 7)) == Set(digits(n)); \\ Michel Marcus, Feb 18 2017

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

More terms from Don Reble, Apr 28 2006

Edited by John Cerkan, Feb 17 2017

cp's OEIS Frontend

A037402 Numbers k such that every base-7 digit of k is a base-8 digit of k.

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A037403 Numbers k such that every base-7 digit of k is a base-9 digit of k.

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A037440 Positive numbers having the same set of digits in base 7 and base 10.

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