A120067 Swap each two consecutive semiprimes.

1, 2, 3, 6, 5, 4, 7, 8, 10, 9, 11, 12, 13, 15, 14, 16, 17, 18, 19, 20, 22, 21, 23, 24, 26, 25, 27, 28, 29, 30, 31, 32, 34, 33, 38, 36, 37, 35, 46, 40, 41, 42, 43, 44, 45, 39, 47, 48, 51, 50, 49, 52, 53, 54, 57, 56, 55, 62, 59, 60, 61, 58, 63, 64, 69, 66, 67, 68, 65, 70, 71, 72

Offset

1,2

Links

Table of n, a(n) for n=1..72.

Example

Start with the sequence of natural numbers:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
First pair of consecutive semiprimes are 4 and 6, swap them:
1,2,3,6,5,4,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
next pair of consecutive semiprimes are 9 and 10, swap them:
1,2,3,6,5,4,7,8,10,9,11,12,13,14,15,16,17,18,19,20,
next pair of consecutive semiprimes are 14 and 15, swap them:
1,2,3,6,5,4,7,8,10,9,11,12,13,15,14,16,17,18,19,20,
etc.

Mathematica

s=Range@200; sp=Select[s, 2==Total[Last/@FactorInteger[ # ]]&]; Do[a=sp[[i]]; b=sp[[i+1]]; s[[a]]=b; s[[b]]=a, {i, 1, 61, 2}]; s

Crossrefs

Cf. A001358.

Sequence in context: A222241 A056023 A133259 * A357522 A089843 A269378

Adjacent sequences: A120064 A120065 A120066 * A120068 A120069 A120070

Keyword

nonn

Author

Zak Seidov, Jun 07 2006

Status

approved