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Semiprimes k with a semiprime number of syllables in their name in American English.
3

%I #19 May 27 2024 22:38:44

%S 57,74,87,106,111,121,122,123,129,133,134,141,142,143,145,146,155,158,

%T 159,161,166,169,183,185,194,201,202,203,205,206,209,217,221,226,235,

%U 249,253,254,259,262,265,289,291,295,298,299,301,302,303,305,309

%N Semiprimes k with a semiprime number of syllables in their name in American English.

%C This is to A163648 as semiprimes A001358 are to primes A000040.

%C The word "and" is excluded, 101 is "one hundred one" rather than "one hundred and one."

%C Number of syllables in n in American English is A075774.

%C See A231073 and A231075 for prime analogs counting words respectively letters.

%H Charles R Greathouse IV, <a href="/A230956/b230956.txt">Table of n, a(n) for n = 1..10000</a>

%F {k: k is in A001358 and A075774(k) is in A001358}.

%e 87 is in the sequence because 87 = 3 * 29 is semiprime, "eighty-seven" has 4 syllables, and 4 = 2^2 is also semiprime.

%e 106 is in the sequence because 106 = 2 * 53 is semiprime and "one hundred six" has semiprime 4 syllables.

%e 111 is in the sequence because 111 = 3 * 37 is semiprime and "one hundred eleven" has semiprime 6 = 2*3 syllables.

%o (Python) # uses function in A075774

%o from sympy import factorint

%o def issemiprime(n): return sum(factorint(n).values()) == 2

%o def ok(n): return issemiprime(A075774(n)) and issemiprime(n)

%o print([k for k in range(310) if ok(k)]) # _Michael S. Branicky_, May 27 2024

%Y Cf. A001358, A075774, A163648, A231073, A231075.

%K nonn,word,easy

%O 1,1

%A _Jonathan Vos Post_, Nov 04 2013

%E Corrected and extended by _Charles R Greathouse IV_, Jan 23 2014