A214522 List of words over {1,5} with equal numbers of 1's and 5's.

15, 51, 1155, 1515, 1551, 5115, 5151, 5511, 111555, 115155, 115515, 115551, 151155, 151515, 151551, 155115, 155151, 155511, 511155, 511515, 511551, 515115, 515151, 515511, 551115, 551151, 551511, 555111

Offset: 1

Author

Jonathan Vos Post, Jul 19 2012

Keywords

• nonn
• base
• easy

Comments

This 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 3, because each pair of "1" and "5" contributes a digital sum of 6, hence the total is divisible by 3.

The subsequence of semiprimes begins 15, 51, 15151551, 51115551, 51515511, 51555111, 55515111, 1115155551, 1115515551, 1151551551,..

Crossrefs

Cf. A214218, A214488, A214521.

Programs

Mathematica

Sort[FromDigits/@Flatten[Table[Permutations[PadRight[{},2n,{1,5}]],{n,3}],1]] (* Harvey P. Dale, Aug 30 2016 *)