A241758 -id:A241758 - cp's OEIS frontend

A241856 Smallest number of carries while adding two primes in binary, the sum of which is 2*n.

1, 2, 3, 2, 3, 2, 4, 3, 2, 1, 3, 3, 2, 1, 5, 2, 3, 3, 3, 2, 2, 1, 4, 3, 3, 1, 3, 1, 2, 2, 6, 5, 6, 2, 3, 3, 2, 1, 4, 3, 2, 2, 3, 1, 2, 1, 5, 5, 2, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 3, 2, 1, 7, 4, 5, 2, 3, 3, 2, 1, 4, 3, 2, 2, 3, 1, 2, 2, 5, 4, 3, 2, 3, 2, 2, 1, 4

Offset: 2

Vladimir Shevelev, Apr 30 2014

			Let n=5. We have 2*5=10=3+7=5+5. Adding 3+7 in binary requires 3 carries, while adding 5+5 in binary requires 2 carries. Thus a(5)=2.

Peter J. C. Moses, Table of n, a(n) for n = 2..1001

Cf. A241757, A241758.

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

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.

Original entry on oeis.org

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

Vladimir Shevelev, Apr 30 2014

nonn

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

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

			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.

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

Cf. A241756, A241758.

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

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

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

cp's OEIS Frontend

A241856 Smallest number of carries while adding two primes in binary, the sum of which is 2*n.

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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.

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