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A110603 Numbers n whose base 5 representations, interpreted as base 10 integers, are semiprimes.

%I A110603 #13 Aug 14 2023 11:34:37
%S A110603 4,5,9,11,12,18,19,31,36,37,38,43,44,46,47,48,51,52,53,58,59,61,76,77,
%T A110603 78,84,86,88,94,96,103,106,108,112,128,131,146,147,148,151,156,159,
%U A110603 161,168,171,172,177,178,181,184,194,196,198,208,212,218,223,226,227,228
%N A110603 Numbers n whose base 5 representations, interpreted as base 10 integers, are semiprimes.
%C A110603 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.
%H A110603 Harvey P. Dale, <a href="/A110603/b110603.txt">Table of n, a(n) for n = 1..1000</a>
%e A110603 a(1) = 4 because 4 (base 5) = 4 and 4 (base 10) = 2 * 2, a semiprime (A001358).
%e A110603 a(2) = 5 because 5 (base 5) = 10 and 10 (base 10) = 2 * 5.
%e A110603 a(3) = 9 because 9 (base 5) = 14 and 14 (base 10) = 2 * 7.
%e A110603 a(4) = 11 because 11 (base 5) = 21 and 21 (base 10) = 3 * 7.
%e A110603 a(5) = 12 because 12 (base 5) = 22 and 22 (base 10) = 2 * 11.
%t A110603 Select[Range[228], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 5]]] == 2 &] (* _Ray Chandler_, Aug 05 2005 *)
%t A110603 Select[Range[300],PrimeOmega[FromDigits[IntegerDigits[#,5],10]]==2&] (* _Harvey P. Dale_, Aug 14 2023 *)
%Y A110603 Cf. A001358, A007091, A108873, A110602, A110604, A110605, A110606, A110607.
%K A110603 base,easy,nonn
%O A110603 1,1
%A A110603 _Jonathan Vos Post_, Jul 30 2005
%E A110603 Corrected and extended by _Ray Chandler_, Aug 05 2005