The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A334931 Numbers that generate rotationally symmetrical XOR-triangles with a pattern of zero-triangles of edge length 2, some of which are clipped to result in some singleton zeros at the edges. 3
 151, 233, 1483, 1693, 10707, 13029, 644007, 941241, 317049751, 490370281, 3111314891, 3550957213, 22455577043, 27325461221, 1350581212071, 1973926386873, 664901519788951, 1028381017273577, 6524900247528907, 7446897021636253, 47092758308252115, 57305645652210405 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subset of A334769 which is a subset of A334556. Numbers m in this sequence A070939(m) (mod 3) = 2. The numbers in this sequence can be constructed using run lengths of bits. 2n has the reverse run length pattern as 2n - 1. a(1) has the run lengths {1, 2, 1, 1, 3}, while a(2) has {3, 1, 1, 2, 1}, etc. For n = 1 (mod 8): 12..(1132)..113; For n = 3 (mod 8): 113..(2113)..2112; For n = 5 (mod 8): 11123..(1123)..1122; For n = 7 (mod 8): 123112..(3112)..31123, where the parenthetic run lengths occur, when they occur, in multiples of 3. Thus, a(9) has the run length form 12113211321132113 = binary 10010111001011100101110010111 = decimal 317049751. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..1264 Michael De Vlieger, Diagram montage of XOR-triangles resulting from a(n) with 1 <= n <= 32. Michael De Vlieger, Central zero-triangles in rotationally symmetrical XOR-Triangles, 2020. EXAMPLE Diagrams of a(1)-a(6), replacing "0" with "." and "1" with "@" for clarity: a(1) = 151 (a(2) = 233 appears as a mirror image):   @ . . @ . @ @ @    @ . @ @ @ . .     @ @ . . @ .      . @ . @ @       @ @ @ .        . . @         . @          @ . a(3) = 1483 (a(4) = 1693 appears as a mirror image):   @ . @ @ @ . . @ . @ @    @ @ . . @ . @ @ @ .     . @ . @ @ @ . . @      @ @ @ . . @ . @       . . @ . @ @ @        . @ @ @ . .         @ . . @ .          @ . @ @           @ @ .            . @             @ . a(5) = 10707 (a(6) = 13029 appears as a mirror image):   @ . @ . . @ @ @ . @ . . @ @    @ @ @ . @ . . @ @ @ . @ .     . . @ @ @ . @ . . @ @ @      . @ . . @ @ @ . @ . .       @ @ . @ . . @ @ @ .        . @ @ @ . @ . . @         @ . . @ @ @ . @          @ . @ . . @ @           @ @ @ . @ .            . . @ @ @             . @ . .              @ @ .               . @                @ MATHEMATICA Array[FromDigits[Flatten@ MapIndexed[ConstantArray[#2, #1] & @@ {#1, Mod[First[#2], 2]} &, If[EvenQ@ #1, Reverse@ #2, #2]], 2] & @@ {#1, Which[#2 == 1, PadRight[{1, 2}, 12 Ceiling[#1/8] - 7, {3, 2, 1, 1}], #2 == 2, PadRight[{1, 1}, 12 Ceiling[#1/8] - 6, {1, 1, 3, 2}]~Join~{2}, #2 == 3, PadRight[{1, 1}, 12 Ceiling[#1/8] - 4, {3, 1, 1, 2}]~Join~{2}, True, PadRight[{}, 12 Ceiling[#1/8] - 1, {1, 2, 3, 1}]]} & @@ {#, Ceiling[Mod[#, 8]/2]} &, 22] (* Generate a textual plot of XOR-triangle T(n) *) xortri[n_Integer] := TableForm@ MapIndexed[StringJoin[ConstantArray[" ", First@ #2 - 1], StringJoin @@ Riffle[Map[If[# == 0, "." (* 0 *), "@" (* 1 *)] &, #1], " "]] &, NestWhileList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, IntegerDigits[n, 2], Length@ # > 1 &]] CROSSREFS Cf. A334556, A334769, A334930, A334932. Sequence in context: A300394 A142225 A334769 * A059858 A152310 A276264 Adjacent sequences:  A334927 A334928 A334930 * A334932 A334933 A334934 KEYWORD nonn,easy AUTHOR Michael De Vlieger, May 16 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 9 13:39 EDT 2020. Contains 336323 sequences. (Running on oeis4.)