A241857 Number of primes p less than prime(n)-1, such that adding prime(n)-1 and p in binary does not require any carry.

0, 0, 2, 0, 1, 2, 6, 2, 0, 2, 0, 5, 7, 2, 1, 3, 1, 2, 8, 2, 9, 1, 4, 5, 11, 5, 1, 2, 4, 6, 0, 14, 16, 7, 9, 3, 4, 6, 3, 6, 3, 5, 0, 18, 8, 2, 4, 0, 4, 5, 7, 1, 6, 1, 54, 10, 15, 5, 16, 18, 7, 14, 6, 3, 10, 5, 6, 16, 2, 4, 17, 2, 1, 6, 1, 0, 15, 8, 19, 10, 6, 9

Offset: 1

Author

Vladimir Shevelev, Apr 30 2014

Keywords

• nonn

Comments

Or the number of primes less than prime(n)-1, such that

A000120(prime(n)+p-1) = A000120(p) + A000120(prime(n)-1).

Examples

			Let n=12. Prime(12)-1=37-1=36. There are only 5 primes less than 36 the adding of which with 36 does not require any carry: 2,3,11,17,19. So a(12)=5.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A241756, A241758.

Programs

Sage

def count(x):
    c = 0
    for y in prime_range(x):
        if binomial(y+x-1,y) % 2:
            c += 1
    return c
[count(i) for i in primes_first_n(100)] # - Tom Edgar, May 01 2014

Formula

For Mersenne prime(n), a(n)=0; for Fermat prime(n)>3, a(n)= n-1.

Extensions

More terms from Peter J. C. Moses, Apr 30 2014