A110194 First differences of A110095 (least nonprime sequence whose first differences are nonprime).

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, 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, 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

Offset

1,2

Comments

Conjecture: from a(5) on, are there only substrings <1 1 4> and <1 1 1 1 4 4 >?

Links

Table of n, a(n) for n=1..95.

Example

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).
Then add 1=10 for a(3).
Then add (not 1 because 11 is prime; nor 2 and 3 because they are prime) ...add 4=14 for a(4), etc.

Prog

(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

Crossrefs

Cf. A110095 and twin-primes related sequences.

Sequence in context: A140457 A358286 A176457 * A199283 A079359 A010156

Adjacent sequences: A110191 A110192 A110193 * A110195 A110196 A110197

Keyword

easy,nonn

Author

Alexandre Wajnberg and Eric Angelini, Sep 06 2005

Extensions

More terms from Michel Marcus, Aug 09 2022

Status

approved