A367848 Lengths >= 2 of symmetrical subsequences within the prime gaps sequence.

2, 3, 5, 5, 3, 9, 5, 2, 3, 3, 3, 5, 3, 3, 5, 2, 11, 2, 3, 3, 2, 3, 2, 3, 2, 3, 5, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 5, 2, 2, 3, 7, 3, 2, 3, 3, 5, 5, 7, 3, 3, 5, 2, 2, 3, 5, 3, 3, 3, 2, 5, 2, 3, 2, 2, 3, 7, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 5

Offset: 1

Author

Tamas Sandor Nagy, Dec 02 2023

Keywords

• nonn

Comments

Points in the primes gap sequence (A001223) are taken successively at a term and halfway between terms.

The lengths here are of subsequences made of 2 or more symmetrically placed, consecutive prime gaps around such a point.

Some points only have a subsequence of length 0 or 1 around them and they are ignored.

Will all odd numbers appear in this sequence?

Do the terms have a long-term average?

Examples

			The first lengths are as follows, around midpoints marked with ".",
  Gaps:  1   2   2   4   2   4   2    = A001223
             \_._/                  length 2 = a(1)
                 \___.___/          length 3 = a(2)
                 \_______._______/  length 5 = a(3)
		

Crossrefs

Cf. A000040, A001223, A081235, A346399, A359440.

Programs

PARI

diff(v) = vector(#v-1, i, v[i+1]-v[i]);
issym(v) = if (#v>1, for (j=1, #v\2, if (v[j] != v[#v-j+1], return(0))); return(1));
lista(nn) = my(v = diff(primes(nn))); for (len=2, #v, for (i=0, len\2, my(w = vector(len-2*i, j, v[i+j])); if (issym(w), print1(#w, ", "); break););); \\ Michel Marcus, Dec 05 2023