OFFSET
1,1
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?
EXAMPLE
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)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Tamas Sandor Nagy, Dec 02 2023
STATUS
approved