A110194 - OEIS

%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