A331102 a(n) is the greatest prime number of the form n mod (2^k) for some k > 0, or 0 if no such prime number exists.

0, 0, 2, 3, 0, 5, 2, 7, 0, 0, 2, 11, 0, 13, 2, 7, 0, 17, 2, 19, 0, 5, 2, 23, 0, 0, 2, 11, 0, 29, 2, 31, 0, 0, 2, 3, 0, 37, 2, 7, 0, 41, 2, 43, 0, 13, 2, 47, 0, 17, 2, 19, 0, 53, 2, 23, 0, 0, 2, 59, 0, 61, 2, 31, 0, 0, 2, 67, 0, 5, 2, 71, 0, 73, 2, 11, 0, 13, 2

Offset: 0

Author

Rémy Sigrist, Jan 09 2020

Keywords

• nonn
• look
• base

Comments

In other words, a(n) is the largest binary prime suffix of n, or 0 if no such suffix exists.

Examples

			For n = 45:
- we have:
  k   45 mod (2^k)  prime?
  --  ------------  ------
   1             1  no
   2             1  no
   3             5  yes
   4            13  yes
   5            13  yes
  >5            45  no
- hence a(45) = 13.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A331097 (decimal analog).

Programs

PARI

a(n, base=2) = my (d=digits(n, base), s); for (k=1, #d, if (isprime(s=fromdigits(d[k..#d], base)), return (s))); 0

Formula

a(n) <= n with equality iff n = 0 or n is a prime number.