A110605 - OEIS

A110605

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

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OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

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