A389238 Odd numbers k whose symmetric representation of sigma, SRS(k), consists of an odd number, >1, of parts and whose center part is the minimum of all parts.

9, 15, 25, 35, 49, 77, 81, 91, 121, 143, 153, 165, 169, 187, 195, 209, 221, 247, 255, 285, 289, 299, 323, 345, 361, 375, 391, 425, 435, 437, 441, 475, 493, 525, 527, 529, 551, 567, 575, 589, 625, 665, 667, 703, 713, 725, 729, 735, 775, 777, 805, 825, 841, 851, 861, 875, 891, 897, 899, 925, 943, 961, 975, 989

Offset

1,1

Comments

All numbers of the form k = p^(2*m), m >=1 and p odd prime, belong to this sequence; for these numbers k, SRS(k) has maximum width 1, consists of 2*m+1 parts and its center part, having size p^m, is a divisor of k; except for number 4, A001248 is a subsequence of these numbers.

Since every number k in this sequence is odd, the first and last part of SRS(k) have width 1.

Conjecture: The width pattern for any k in this sequence for which SRS(k) consists of three parts is 10101 or 1012101; in addition, these numbers k form sequence A087718(n), n >= 3.

Links

Table of n, a(n) for n=1..64.

Example

a(1) = 9 is the smallest odd number whose symmetric representation of sigma consists of more than 2 parts and SRS(9) = {5, 3, 5}.
45 is the smallest odd number, whose symmetric representation of sigma consists of at least 3 parts, that does not belong to this sequence since SRS(45) = {23, 32, 23}.

Mathematica

(* Function partsSRS[ ] is defined in A377654 *)
a389238Q[n_] := Module[{ps=partsSRS[n], len}, len=Length[ps]; OddQ[n]&&OddQ[len]&& len>2&&ps[[(len+1)/2]]==Min[ps]]
a389238[n_] := Select[Range[n], a389238Q]
a389238[1000]

Crossrefs

Cf. A003056, A087718, A235791, A237048, A237591, A237593, A249223, A377654.

Sequence in context: A227198 A279102 A319529 * A249730 A342418 A251415

Adjacent sequences: A389235 A389236 A389237 * A389239 A389240 A389241

Keyword

nonn

Author

Hartmut F. W. Hoft, Oct 28 2025

Status

approved