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

%I A367848 #60 Jan 24 2024 23:49:21
%S A367848 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,
%T A367848 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,
%U A367848 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
%N A367848 Lengths >= 2 of symmetrical subsequences within the prime gaps sequence.
%C A367848 Points in the primes gap sequence (A001223) are taken successively at a term and halfway between terms.
%C A367848 The lengths here are of subsequences made of 2 or more symmetrically placed, consecutive prime gaps around such a point.
%C A367848 Some points only have a subsequence of length 0 or 1 around them and they are ignored.
%C A367848 Will all odd numbers appear in this sequence?
%C A367848 Do the terms have a long-term average?
%e A367848 The first lengths are as follows, around midpoints marked with ".",
%e A367848   Gaps:  1   2   2   4   2   4   2    = A001223
%e A367848              \_._/                  length 2 = a(1)
%e A367848                  \___.___/          length 3 = a(2)
%e A367848                  \_______._______/  length 5 = a(3)
%o A367848 (PARI) diff(v) = vector(#v-1, i, v[i+1]-v[i]);
%o A367848 issym(v) = if (#v>1, for (j=1, #v\2, if (v[j] != v[#v-j+1], return(0))); return(1));
%o A367848 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
%Y A367848 Cf. A000040, A001223, A081235, A346399, A359440.
%K A367848 nonn
%O A367848 1,1
%A A367848 _Tamas Sandor Nagy_, Dec 02 2023