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

3, 8, 39, 269, 3047, 14288, 140205, 1567591, 10764655, 83804613, 977368042

Offset

1,1

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

Links

Table of n, a(n) for n=1..11.

Sean A. Irvine, Java program (github)

Example

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.

Prog

(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

Crossrefs

Cf. A072686.

Sequence in context: A180368 A108262 A034892 * A353718 A260817 A262126

Adjacent sequences: A072684 A072685 A072686 * A072688 A072689 A072690

Keyword

nonn,word,more

Author

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

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

a(10) from Michael S. Branicky, Dec 24 2025

a(11) from Michael S. Branicky, Jan 02 2026

Status

approved