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.

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

0,1

Comments

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.

Links

Table of n, a(n) for n=0..65.

Formula

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.

Example

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.

Mathematica

(* 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]

Crossrefs

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

Sequence in context: A360929 A228068 A182233 * A239282 A171015 A244571

Adjacent sequences: A370201 A370202 A370203 * A370205 A370206 A370207

Keyword

nonn

Author

Hartmut F. W. Hoft, Feb 11 2024

Status

approved