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A072687 Number of primes with prime length names in range 1 -> 10^n. 2

%I #17 Mar 18 2021 18:00:49

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

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

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

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a072/A072687.java">Java program</a> (github)

%e 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.

%e 23 ("twentythree", 11 letters) and 109 ("one hundred and nine", 17 letters) are counted.

%o (Python)

%o from num2words import num2words

%o from sympy import isprime, primerange

%o def n2w(n):

%o return num2words(n).replace(",", "").replace(" ", "").replace("-", "")

%o def a(n): return sum(isprime(len(n2w(p))) for p in primerange(2, 10**n))

%o print([a(n) for n in range(1, 7)]) # _Michael S. Branicky_, Mar 08 2021

%Y Cf. A072686.

%K more,nonn,word

%O 1,1

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

%E a(6)-a(8) from _Sean A. Irvine_, Nov 08 2011

%E a(8) corrected by _Sean A. Irvine_, Apr 28 2019

%E a(8) corrected and a(9) from _Michael S. Branicky_, Mar 08 2021

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Last modified April 19 05:19 EDT 2024. Contains 371782 sequences. (Running on oeis4.)