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

0,3

Comments

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

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A331097 (decimal analog).

Sequence in context: A339694 A074722 A370744 * A080368 A057174 A197658

Adjacent sequences: A331099 A331100 A331101 * A331103 A331104 A331105

Keyword

nonn,look,base

Author

Rémy Sigrist, Jan 09 2020

Status

approved