

A247253


First differences of A251239.


11



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
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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 !! (n1)
a247253_list = zipWith () (tail a251239_list) a251239_list


CROSSREFS

Cf. A251239, A098550, A002808, A251417, A251549.
Sequence in context: A082796 A078245 A241057 * A244293 A196737 A070058
Adjacent sequences: A247250 A247251 A247252 * A247254 A247255 A247256


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Dec 02 2014


STATUS

approved



