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%I #10 Aug 09 2022 05:41:23
%S 1,8,1,4,1,1,4,1,1,4,1,1,4,1,1,1,1,4,4,1,1,4,1,1,4,1,1,4,1,1,1,1,4,4,
%T 1,1,1,1,4,4,1,1,4,1,1,1,1,4,4,1,1,4,1,1,4,1,1,1,1,1,1,1,1,1,1,4,4,1,
%U 1,4,1,1,1,1,1,1,1,1,4,1,1,1,1,4,1,1,4,4,1,1,4,1,1,4,1
%N First differences of A110095 (least nonprime sequence whose first differences are nonprime).
%C Conjecture: from a(5) on, are there only substrings <1 1 4> and <1 1 1 1 4 4 >?
%e Beginning with 1, we have to add 8 in order to get the first nonprime number (all other numbers <8 are prime or giving a prime). So 1+8=9 for a(2).
%e Then add 1=10 for a(3).
%e Then add (not 1 because 11 is prime; nor 2 and 3 because they are prime) ...add 4=14 for a(4), etc.
%o (PARI) lista(nn) = my(va = vector(nn), last=0); for (n=1, nn, my(new = last+1); while(isprime(new) || isprime(new-last), new++); va[n] = new-last; last = new;); va; \\ _Michel Marcus_, Aug 09 2022
%Y Cf. A110095 and twin-primes related sequences.
%K easy,nonn
%O 1,2
%A _Alexandre Wajnberg_ and _Eric Angelini_, Sep 06 2005
%E More terms from _Michel Marcus_, Aug 09 2022
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