A072687 Number of primes with prime length names in range 1 -> 10^n.

3, 8, 39, 269, 3047, 14288, 140205, 1567591, 10764655

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jul 02 2002

Keywords

• more
• nonn
• word

Comments

This sequence uses "and" (e.g., "one hundred and one") and does not count spaces, commas, or hyphens. - Michael S. Branicky, Mar 08 2021

Examples

			E.g., from the sequence of the valid primes (A072686) there are three prime-length primes between 1 and 10: 2,3,7; therefore a(1)=3.
23 ("twentythree", 11 letters) and 109 ("one hundred and nine", 17 letters) are counted.
		

Links

• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A072686.

Programs

Python

from num2words import num2words
from sympy import isprime, primerange
def n2w(n):
  return num2words(n).replace(chr(44), "").replace(" ", "").replace("-", "")
def a(n): return sum(isprime(len(n2w(p))) for p in primerange(2, 10**n))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Mar 08 2021

Extensions

a(6)-a(8) from Sean A. Irvine, Nov 08 2011

a(8) corrected by Sean A. Irvine, Apr 28 2019

a(8) corrected and a(9) from Michael S. Branicky, Mar 08 2021