A164702 Write n in binary. Insert one 0 right of any one 1. a(n) is the smallest possible composite equal to the value of any such resulting binary number.

4, 6, 8, 9, 10, 14, 16, 18, 18, 21, 20, 21, 22, 27, 32, 33, 34, 35, 36, 42, 38, 39, 40, 49, 42, 51, 44, 45, 46, 55, 64, 65, 66, 69, 68, 69, 70, 75, 72, 81, 74, 75, 76, 77, 78, 87, 80, 81, 82, 99, 84, 85, 86, 87, 88, 105, 90, 91, 92, 93, 94, 95, 128, 129, 130, 133, 132, 133, 134

Offset: 2

Author

Leroy Quet, Aug 22 2009

Keywords

• base
• nonn

Examples

			9 in binary is 1001. Putting a 0 after the first 1 results in 10001, which is 17 in decimal. Putting a 0 after the last 1 results in 10010, which is 18 in decimal. 17 is < 18, but 17 is prime. So a(9) = 18, a composite.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..16384

Programs

Maple

rebase := proc(L,b) add( op(i,L)*b^(i-1),i=1..nops(L)) ; end proc: A164702 := proc(n) local bdg,a,p,bplu,newa ; bdg := convert(n,base,2) ; a := -1 ; for p from 1 to nops(bdg) do if op(p,bdg) = 1 then bplu := [op(1..p-1,bdg),0,op(p..nops(bdg),bdg)] ; newa := rebase(bplu,2) ; if newa > 3 and not isprime(newa) then if a = -1 or newa < a then a := newa ; end if; end if; end if; end do ; return a ; end proc: seq(A164702(n),n=2..100) ; # R. J. Mathar, Feb 27 2010

Mathematica

Table[With[{d = IntegerDigits[n, 2]}, SelectFirst[Map[FromDigits[#, 2] &@ Insert[d, 0, # + 1] &, Position[d, 1]], CompositeQ]], {n, 2, 70}] (* Michael De Vlieger, Sep 03 2017 *)

Extensions

Terms beyond a(13) from R. J. Mathar, Feb 27 2010