A230956 Semiprimes k with a semiprime number of syllables in their name in American English.

57, 74, 87, 106, 111, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 183, 185, 194, 201, 202, 203, 205, 206, 209, 217, 221, 226, 235, 249, 253, 254, 259, 262, 265, 289, 291, 295, 298, 299, 301, 302, 303, 305, 309

Offset: 1

Author

Jonathan Vos Post, Nov 04 2013

Keywords

• nonn
• word
• easy

Comments

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

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

Number of syllables in n in American English is A075774.

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

Examples

			87 is in the sequence because 87 = 3 * 29 is semiprime, "eighty-seven" has 4 syllables, and 4 = 2^2 is also semiprime.
106 is in the sequence because 106 = 2 * 53 is semiprime and "one hundred six" has semiprime 4 syllables.
111 is in the sequence because 111 = 3 * 37 is semiprime and "one hundred eleven" has semiprime 6 = 2*3 syllables.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Python

# uses function in A075774
from sympy import factorint
def issemiprime(n): return sum(factorint(n).values()) == 2
def ok(n): return issemiprime(A075774(n)) and issemiprime(n)
print([k for k in range(310) if ok(k)]) # Michael S. Branicky, May 27 2024

Formula

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

Extensions

Corrected and extended by Charles R Greathouse IV, Jan 23 2014