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

2,1

Links

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

Example

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.

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 *)

Crossrefs

Sequence in context: A346041 A341614 A323644 * A001745 A359982 A276628

Adjacent sequences: A164699 A164700 A164701 * A164703 A164704 A164705

Keyword

base,nonn

Author

Leroy Quet, Aug 22 2009

Extensions

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

Status

approved