A247253 - OEIS

%I #38 Dec 25 2014 13:21:59

%S 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,

%T 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,

%U 11,7,13,9,9,17,31,7,7,9,29,9,25,5,7,13,15,15,11

%N First differences of A251239.

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

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

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

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

%C Conjecture 4: a(n) = A251417(n+5) for n>7. (The first four conjectures are due to _Reinhard Zumkeller_.)

%C 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

%H Reinhard Zumkeller, <a href="/A247253/b247253.txt">Table of n, a(n) for n = 1..10000</a>

%o (Haskell)

%o a247253 n = a247253_list !! (n-1)

%o a247253_list = zipWith (-) (tail a251239_list) a251239_list

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

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Dec 02 2014