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A247253 First differences of A251239.

%I A247253 #38 Dec 25 2014 13:21:59
%S A247253 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 A247253 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 A247253 11,7,13,9,9,17,31,7,7,9,29,9,25,5,7,13,15,15,11
%N A247253 First differences of A251239.
%C A247253 a(n) = A251239(n+1) - A251239(n);
%C A247253 Conjecture 1: a(n) > 0, since presumably primes occur in A098550 in natural order;
%C A247253 Conjecture 2: it seems that a(n) = 1 only for n = 1, 5, 10 and 13;
%C A247253 Conjecture 3: a(n) - 1 = number of composite terms between prime(n) and prime(n+1) in A098550;
%C A247253 Conjecture 4: a(n) = A251417(n+5) for n>7. (The first four conjectures are due to _Reinhard Zumkeller_.)
%C A247253 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 A247253 Reinhard Zumkeller, <a href="/A247253/b247253.txt">Table of n, a(n) for n = 1..10000</a>
%o A247253 (Haskell)
%o A247253 a247253 n = a247253_list !! (n-1)
%o A247253 a247253_list = zipWith (-) (tail a251239_list) a251239_list
%Y A247253 Cf. A251239, A098550, A002808, A251417, A251549.
%K A247253 nonn
%O A247253 1,2
%A A247253 _Reinhard Zumkeller_, Dec 02 2014