A110095 Least increasing sequence of nonprimes whose first differences are also nonprime.

0, 1, 9, 10, 14, 15, 16, 20, 21, 22, 26, 27, 28, 32, 33, 34, 35, 36, 40, 44, 45, 46, 50, 51, 52, 56, 57, 58, 62, 63, 64, 65, 66, 70, 74, 75, 76, 77, 78, 82, 86, 87, 88, 92, 93, 94, 95, 96, 100, 104, 105, 106, 110, 111, 112, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125

Offset

1,3

Comments

The sequence of first differences contains only 1's and 4's (with an 8 at the beginning): 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

Links

Table of n, a(n) for n=1..65.

Example

Begin with a(1)=0. Add to a(1) the least nonprime giving a nonprime number: + 1 = 1 for a(2). Now add to a(2) the least nonprime giving a composite: + 8 = 9 for a(3). Same rule: + 1 = 10 for a(4). Same rule: + 4 = 14 etc...

Mathematica

f[s_List] := Block[{j = s[[ -1]]}, k = j + 1; While[PrimeQ[k] || PrimeQ[k - j], k++ ]; Append[s, k]]; Nest[f, {0}, 64] (* Robert G. Wilson v, Sep 23 2006 *)

Prog

(PARI) lista(nn) = my(va = vector(nn), last=0); for (n=2, nn, my(new = last+1); while(isprime(new) || isprime(new-last), new++); va[n] = new; last = new; ); va; \\ Michel Marcus, Aug 09 2022

Crossrefs

Cf. A109888, A110194 (first differences).

Sequence in context: A189834 A248350 A247512 * A061445 A369641 A169870

Adjacent sequences: A110092 A110093 A110094 * A110096 A110097 A110098

Keyword

easy,nonn

Author

Alexandre Wajnberg and Eric Angelini, Sep 04 2005

Extensions

Extended by Ray Chandler, Sep 06 2005

Status

approved