A135093 Least composite number k for each possible difference gpf(k)-lpf(k).

4, 6, 15, 10, 21, 14, 55, 33, 22, 39, 26, 85, 51, 34, 57, 38, 115, 69, 46, 203, 145, 87, 58, 93, 62, 259, 185, 111, 74, 205, 123, 82, 129, 86, 235, 141, 94, 371, 265, 159, 106, 413, 295, 177, 118, 183, 122, 469, 335, 201, 134, 355, 213, 142, 219, 146, 553, 395, 237

Offset

0,1

Comments

Clearly all terms are semiprimes. a(0)=prime(1)^2=4. For n>=1, a(n)=k, a squarefree semiprime, where gpf(k)-lpf(k)=A006530(k)-A020639(k)=A030173(k).

For n > 0: first occurrences of A030173(n) in A046665. - Reinhard Zumkeller, Jul 03 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Example

a(3)=2*5=10 because 5-2=3=A030173(3), where the latter terms are ordered by the increasing possible differences between two distinct primes and no smaller composite number has a difference of 3 between its least and greatest prime factors.

Prog

(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a135093 0 = 4
a135093 n = (+ 1) $ fromJust $ (`elemIndex` a046665_list) $ a030173 n
-- Reinhard Zumkeller, Jul 03 2015

Crossrefs

Cf. A001358, A006881, A030173, A020639, A006530.

Cf. A046665.

Sequence in context: A357808 A365074 A284123 * A141667 A048753 A055719

Adjacent sequences: A135090 A135091 A135092 * A135094 A135095 A135096

Keyword

nonn

Author

Rick L. Shepherd, Nov 18 2007

Status

approved