A370204 - OEIS

%I #7 Feb 17 2024 12:43:53

%S 3,5,7,22,11,13,34,17,19,46,23,87,58,29,31,111,74,37,82,41,43,94,47,

%T 159,106,53,177,118,59,61,201,134,67,142,71,73,237,158,79,166,83,267,

%U 178,89,388,291,194,97,202,101,103,214,107,109,226,113,889,762,635,508,381,254,127,262,131,411

%N 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.

%C Indices of the first occurrence of value 2*n in A368945.

%C SRS(a(n)) has an even number of parts.

%C 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.

%C Conjecture: a(n) != -1 for all n >= 0.

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

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

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

%e a(3) = 22 since 22 is the smallest number whose central extent of width 0 equals 6.

%t (* Function extent0[ ] is defined in A368945 *)

%t smallest[n_] := NestWhile[#+1&, n, extent0[#]!=n&]/;EvenQ[n]

%t a370204[n_] := Map[smallest[2#]&, Range[0, n]]

%t a370204[65]

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

%K nonn

%O 0,1

%A _Hartmut F. W. Hoft_, Feb 11 2024