A110603 - OEIS

A110603

Numbers n whose base 5 representations, interpreted as base 10 integers, are semiprimes.

4, 5, 9, 11, 12, 18, 19, 31, 36, 37, 38, 43, 44, 46, 47, 48, 51, 52, 53, 58, 59, 61, 76, 77, 78, 84, 86, 88, 94, 96, 103, 106, 108, 112, 128, 131, 146, 147, 148, 151, 156, 159, 161, 168, 171, 172, 177, 178, 181, 184, 194, 196, 198, 208, 212, 218, 223, 226, 227, 228

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OFFSET

1,1

COMMENTS

A108873 is the equivalent using base 3. A110602 is the equivalent using base 4. A110604 is the equivalent using base 6. A110605 is the equivalent using base 7. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1) = 4 because 4 (base 5) = 4 and 4 (base 10) = 2 * 2, a semiprime (A001358).

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

a(3) = 9 because 9 (base 5) = 14 and 14 (base 10) = 2 * 7.

a(4) = 11 because 11 (base 5) = 21 and 21 (base 10) = 3 * 7.

a(5) = 12 because 12 (base 5) = 22 and 22 (base 10) = 2 * 11.

MATHEMATICA

Select[Range[228], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 5]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)

Select[Range[300], PrimeOmega[FromDigits[IntegerDigits[#, 5], 10]]==2&] (* Harvey P. Dale, Aug 14 2023 *)

CROSSREFS