editing

approved

Select[Range[187], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 7]]] == 2 &] (* _Ray Chandler_, Aug 05 2005 *)

approved

editing

_Jonathan Vos Post (jvospost3(AT)gmail.com), _, Jul 30 2005

Extended by _Ray Chandler (rayjchandler(AT)sbcglobal.net), _, Aug 05 2005

a(3) = 7 because 7 (base 7) = 10, and 10 (base 10) = 2 * 5.

a(4) = 11 because 11 (base 7) = 14, and 14 (base 10) = 2 * 7.

a(5) = 12 because 12 (base 7) = 15, and 15 (base 10) = 3 * 5.

base,easy,nonn,new

base,easy,nonn,new

Jonathan Vos Post (jvospost2jvospost3(AT)yahoogmail.com), Jul 30 2005

base,easy,nonn,new

Extended by Ray Chandler (RayChandlerrayjchandler(AT)alumni.tcusbcglobal.edunet), Aug 05 2005

Numbers n whose base 7 representations, interpreted as base 10 integers, are semiprimes.

4, 6, 7, 11, 12, 15, 16, 19, 20, 24, 25, 26, 34, 36, 40, 44, 47, 55, 57, 61, 64, 65, 66, 73, 74, 78, 79, 80, 82, 83, 89, 92, 97, 99, 100, 101, 103, 104, 108, 109, 110, 113, 118, 124, 136, 137, 142, 145, 148, 149, 150, 152, 158, 162, 164, 167, 172, 173, 176, 181, 187

1,1

A108873 is the equivalent using base 3. A110602 is the equivalent using base 4. A110603 is the equivalent using base 5. A110604 is the equivalent using base 6. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

a(1) = 4 because 4 (base 7) = 4 (base 10) = 2 * 2, a semiprime (A001358).

a(2) = 6 because 6 (base 7) = 6 (base 10) = 2 * 3

a(3) = 7 because 7 (base 7) = 10, and 10 (base 10) = 2 * 5.

a(4) = 11 because 11 (base 7) = 14, and 14 (base 10) = 2 * 7.

a(5) = 12 because 12 (base 7) = 15, and 15 (base 10) = 3 * 5.

Select[Range[187], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 7]]] == 2 &] (*Chandler*)

Cf. A001358, A007093, A108873, A110602, A110603, A110604, A110606, A110607.

base,easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jul 30 2005

Extended by Ray Chandler (RayChandler(AT)alumni.tcu.edu), Aug 05 2005

approved