A214530 -id:A214530 - cp's OEIS frontend

A214531 List of words over {1,8} with equal numbers of 1's and 8's.

18, 81, 1188, 1818, 1881, 8118, 8181, 8811, 111888, 118188, 118818, 118881, 181188, 181818, 181881, 188118, 188181, 188811, 811188, 811818, 811881, 818118, 818181, 818811, 881118, 881181, 881811, 888111

Offset: 1

Jonathan Vos Post, Jul 20 2012

This is to 8 as A214530 is to 7, as A214530 is to 6, as A214522 is to 5, as A214521 is to 4, as A214488 is to 3, and as A214218 is to 2. All of these, interpreted as decimal integers are divisible by 9, because each pair of "1" and "8" contributes a digital sum of 9, hence the total is divisible by 9.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A214218, A214488, A214521, A214522, A214524, A214530.

With[{tb=Table[Join[PadRight[{},n,1],PadRight[{},n,8]],{n,3}]},FromDigits/@ Flatten[Permutations/@tb,1]] (* Harvey P. Dale, Jan 17 2014 *)

A214532 List of words over {1,9} with equal numbers of 1's and 9's.

Original entry on oeis.org

19, 91, 1199, 1919, 1991, 9119, 9191, 9911, 111999, 119199, 119919, 119991, 191199, 191919, 191991, 199119, 199191, 199911, 911199, 911919, 911991, 919119, 919191, 919911, 991119, 991191, 991911, 999111, 11119999, 11191999

Offset: 1

Jonathan Vos Post, Jul 20 2012

This is to 9 as A214531 is to 8, as A214530 is to 7, as A214530 is to 6, as A214522 is to 5, as A214521 is to 4, as A214488 is to 3, and as A214218 is to 2.

The subsequence of primes (when interpreted as decimal integers) is A087515.

Cf. A214218, A214488, A214521, A214522, A214524, A214530, A214531.

FromDigits/@(Flatten[Permutations/@Table[Join[Table[1,{n}],Table[9,{n}]],{n,4}],1]) (* Harvey P. Dale, Aug 20 2014 *)

cp's OEIS Frontend

A214531 List of words over {1,8} with equal numbers of 1's and 8's.

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