A078833 Greatest prime contained as binary substring in binary representation of n>1, a(1)=1.

1, 2, 3, 2, 5, 3, 7, 2, 2, 5, 11, 3, 13, 7, 7, 2, 17, 2, 19, 5, 5, 11, 23, 3, 3, 13, 13, 7, 29, 7, 31, 2, 2, 17, 17, 2, 37, 19, 19, 5, 41, 5, 43, 11, 13, 23, 47, 3, 17, 3, 19, 13, 53, 13, 23, 7, 7, 29, 59, 7, 61, 31, 31, 2, 2, 2, 67, 17, 17, 17, 71, 2, 73, 37, 37, 19, 19, 19, 79, 5, 17

Offset: 1

Author

Reinhard Zumkeller, Dec 08 2002

Keywords

• nonn
• base

Comments

a(n) = A039634(n) for n<=44, but a(45) = 13 <> 11 = A039634(45);

for n>1: a(n) = n iff n is prime.

a(n) = A225243(n, A078826(n)). - Reinhard Zumkeller, Aug 14 2013

Examples

			n=12 -> '1100' contains 2 binary substrings which are primes: '11' (11bb) and '10' (b11b); 3='11' is the greater one, therefore a(12)=3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A078832, A078826, A078822, A007088, A006530.

Programs

Haskell

a078833 = last . a225243_row  -- Reinhard Zumkeller, Aug 14 2013