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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

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

LINKS

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

FORMULA

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

EXAMPLE

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.

PROG

(Sage)

def count(x):

...c=0

...for y in range(x):

......if is_prime(y) and binomial(y+x-1, y).mod(2)==1:

.........c=c+1

...return c

[count(i) for i in primes_first_n(100)] # - Tom Edgar, May 01 2014

CROSSREFS

Cf. A241756, A241758.

Sequence in context: A180662 A318144 A260663 * A300485 A014511 A210572

Adjacent sequences:  A241854 A241855 A241856 * A241858 A241859 A241860

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Apr 30 2014

EXTENSIONS

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

STATUS

approved

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Last modified January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)