A154115 -id:A154115 - cp's OEIS frontend

A370204 a(n) is the smallest number k for which the length of the central extent of width 0 in the symmetric representation of sigma, SRS(k), equals 2n and is -1 if there is no such extent of length 2n.

3, 5, 7, 22, 11, 13, 34, 17, 19, 46, 23, 87, 58, 29, 31, 111, 74, 37, 82, 41, 43, 94, 47, 159, 106, 53, 177, 118, 59, 61, 201, 134, 67, 142, 71, 73, 237, 158, 79, 166, 83, 267, 178, 89, 388, 291, 194, 97, 202, 101, 103, 214, 107, 109, 226, 113, 889, 762, 635, 508, 381, 254, 127, 262, 131, 411

Offset: 0

Hartmut F. W. Hoft, Feb 11 2024

nonn

Indices of the first occurrence of value 2*n in A368945.
SRS(a(n)) has an even number of parts.
The maximum possible central 0 width extent in SRS(n) for odd numbers n is 2*n - (n+1) - 2 = n - 3. This is achieved only by odd prime numbers which form a subsequence.
Conjecture: a(n) != -1 for all n >= 0.

			a(2) = 7 since prime 7 is the smallest number whose central extent of width 0 equals 4.
a(3) = 22 since 22 is the smallest number whose central extent of width 0 equals 6.

Cf. A000040, A071561, A071562, A086801, A100484, A154115, A235791, A237048, A237270, A237593, A249223, A368945.

(* Function extent0[ ] is defined in A368945 *)
smallest[n_] := NestWhile[#+1&, n, extent0[#]!=n&]/;EvenQ[n]
a370204[n_] := Map[smallest[2#]&, Range[0, n]]
a370204[65]

a(n) = min( k : A368945(k) = 2*n ), 0<=n, if the minimum exists, a(n) = -1 otherwise.

A368945(a(k)) = 2 * k, k>=0 and a(k) != -1.

cp's OEIS Frontend

A370204 a(n) is the smallest number k for which the length of the central extent of width 0 in the symmetric representation of sigma, SRS(k), equals 2n and is -1 if there is no such extent of length 2n.

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cp's OEIS Frontend

A370204 a(n) is the smallest number k for which the length of the central extent of width 0 in the symmetric representation of sigma, SRS(k), equals 2*n and is -1 if there is no such extent of length 2*n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula

A370204 a(n) is the smallest number k for which the length of the central extent of width 0 in the symmetric representation of sigma, SRS(k), equals 2n and is -1 if there is no such extent of length 2n.