A247253 First differences of A251239.

1, 6, 6, 7, 1, 7, 13, 8, 10, 1, 17, 8, 1, 13, 13, 13, 5, 10, 11, 5, 9, 8, 19, 10, 11, 7, 11, 5, 9, 27, 9, 13, 5, 23, 5, 9, 17, 9, 11, 11, 7, 21, 9, 7, 5, 17, 27, 11, 7, 9, 17, 5, 13, 9, 21, 11, 7, 13, 9, 9, 17, 31, 7, 7, 9, 29, 9, 25, 5, 7, 13, 15, 15, 11

Offset: 1

Author

Reinhard Zumkeller, Dec 02 2014

Keywords

• nonn

Comments

a(n) = A251239(n+1) - A251239(n);

Conjecture 1: a(n) > 0, since presumably primes occur in A098550 in natural order;

Conjecture 2: it seems that a(n) = 1 only for n = 1, 5, 10 and 13;

Conjecture 3: a(n) - 1 = number of composite terms between prime(n) and prime(n+1) in A098550;

Conjecture 4: a(n) = A251417(n+5) for n>7. (The first four conjectures are due to Reinhard Zumkeller.)

Conjecture 5: Apart from first term, this is equal to the sequence of run lengths in A251549. These run lengths begin 2, 6, 6, 7, 1, 7, 13, 8, 10, 1, 17, 8, 1, 13, 13, 13, 5, 10, 11, 5, 9, ... . - N. J. A. Sloane, Dec 18 2014

Links

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

Crossrefs

Cf. A251239, A098550, A002808, A251417, A251549.

Programs

Haskell

a247253 n = a247253_list !! (n-1)
a247253_list = zipWith (-) (tail a251239_list) a251239_list