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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
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
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 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
CROSSREFS
Sequence in context: A318144 A355297 A260663 * A342020 A300485 A014511
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 30 2014
EXTENSIONS
More terms from Peter J. C. Moses, Apr 30 2014
STATUS
approved