A247253 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

PROG

(Haskell)

a247253 n = a247253_list !! (n-1)

a247253_list = zipWith (-) (tail a251239_list) a251239_list

CROSSREFS

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

Sequence in context: A241057 A375657 A375640 * A244293 A196737 A070058

Adjacent sequences: A247250 A247251 A247252 * A247254 A247255 A247256

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 02 2014

STATUS

approved