A391474 - OEIS

%I #16 Feb 23 2026 22:55:33

%S 9,15,21,25,27,33,35,45,105,770,5950,31815,32445,33705,442365

%N Numbers k for which the symmetric representation of sigma, SRS(k), has at least 3 parts and all positive differences between two parts are at most 10, or all parts have the same size.

%C Sequence A251820 is a subsequence of this sequence.

%C For all numbers k in the sequence found so far SRS(k) has either 3 or 4 parts and thus only one single positive difference of two parts.

%C The next entry in this sequence is larger than 10^7.

%C For numbers k computed so far in this sequence only differences 0, 2, 6, 8, 9 and 10 occur in SRS(k) while differences 1, 3, 4, 5 and 7 appear to occur only together with differences larger than 10.

%e Numbers belonging to this sequence:

%e A251820(1) = 15 since SRS(15) = { 8, 8, 8 }.

%e 21 since in SRS(21) = { 11, 5, 5, 11 } number 6 is the only positive difference of two parts.

%e 770 since SRS(770) = { 579, 570, 579 } has 9 as the only positive difference.

%e A251820(2) = 5950 since SRS(5950) = { 4464, 4464, 4464 }.

%e Number 117 is not in this sequence. Though SRS(117) = { 59, 21, 22, 21, 59 } has 1 as its smallest positive difference, the other positive differences exceed 10.

%e Table of first occurrence of difference 0 <= d <= 10 of any 2 parts for numbers k <= 10^7:

%e   difference:  0  1  2  3  4  5  6  7  8  9  10

%e   ---------------------------------------------

%e   smallest k:  15 -  9  -  -  -  21 -  25 45 33

%t (* Function partsSRS[ ] is defined in A377654 *)

%t diffs[ps_, half_] := Union[Flatten[Map[Abs[ps-RotateLeft[ps, #]]&, Range[half]]]]

%t allDiffsPartsQ[k_, d_] := Module[{ps=partsSRS[k], len}, len=Length[ps]; Length[ps]>2&&AllTrue[diffs[ps, (len+Boole[OddQ[len]])/2 ], #<=d&]]

%t a391474[b_, d_] := Select[Range[b], allDiffsPartsQ[#, d]&]

%t a391474[33705, 10] (* long computation time for 442365 *)

%Y Cf. A237270, A237271, A237593, A251820, A377654, A391475.

%K nonn,more

%O 1,1

%A _Hartmut F. W. Hoft_, Dec 10 2025