login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A246259 Square array: row n contains in ascending order all natural numbers k for which A246271(k)+1 = n, i.e., numbers m for which we need n-1 additional iterations of A003961, starting from A003961(m), before the result is 1 modulo 4. 8
1, 3, 2, 4, 7, 5, 9, 8, 6, 66, 10, 15, 17, 70, 91, 11, 18, 20, 94, 197, 55, 12, 19, 24, 186, 259, 155, 21, 13, 22, 26, 187, 364, 220, 84, 46, 14, 28, 41, 199, 377, 238, 87, 184, 1362, 16, 29, 45, 237, 413, 467, 189, 414, 1981, 1654, 23, 32, 54, 262, 479, 495, 309, 445, 2378, 3055, 1419 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
The topmost row, which has row number 1, is the sequence A246261 (numbers n such that A003961(n) is of the form 4k+1), as these are exactly the numbers that do not require any additional iterations of A003961 for the result to be of the form 4k+1 (because it already is of that form).
If a number k occurs in any particular row, then 4k, 9k, 16k, etc. also occur on the same row, because multiplying a number by a perfect square does not affect the result when it is reduced modulo 4.
The array has an infinite number of rows, provided that A246271 is not bounded, because if A246271(n) = k > 0 for some n, then A246271(A003961(n)) = k-1, thus all the preceding rows would also have terms. However, if A246271 really had an absolute maximum m, then we can consider the array to have just m rows. In either case, all the natural numbers occur in it, each just once, thus the sequence forms a permutation of natural numbers.
Applying A003961 to the terms of any row below the first row gives a subsequence of the immediately preceding row.
LINKS
EXAMPLE
The top left corner of the array:
1, 3, 4, 9, 10, 11, 12, 13, 14, 16, 23, 25, ...
2, 7, 8, 15, 18, 19, 22, 28, 29, 32, 43, 50, ...
5, 6, 17, 20, 24, 26, 41, 45, 54, 57, 61, 68, ...
66, 70, 94, 186, 187, 199, 237, 262, 264, 278, 280, 286, ...
91 197, 259, 364, 377, 413, 479, 627, 665, 669, 705, 763, ...
55, 155, 220, 238, 467, 495, 497, 526, 535, 543, 620, 880, ...
21, 84, 87, 189, 309, 336, 348, 358, 463, 525, 679, 756, ...
...
2 is the least number k such that A003961(k) = 3 modulo 4, but A003961(A003961(k)) = 1 modulo 4 (as indeed A003961(2) = 3, and A003961(3) = 5). Thus A(2,1) = 2.
7 is the second smallest number k satisfying the same property, as A003961(7) = 11 (= 3 mod 4) while A003961(11) = 13 (= 1 mod 4). Thus A(2,2) = 7.
8 is the third smallest number k satisfying the same property, as A003961(8)=27 ( = 3 mod 4) while A003961(27) = 125 = 1 mod 4. Thus A(2,3) = 8.
5 is the least number k such that both A003961(k) and A003961(A003961(k)) = 3 mod 4 but A003961(A003961(A003961(k))) = 1 mod 4. Indeed A003961(5) = 7, A003961(7) = 11 and only at A003961(11) = 13 = 1 mod 4. Thus A(3,1) = 5.
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define (A246259 n) (A246259bi (A002260 n) (A004736 n)))
(define (A246259bi row col) ((rowfun-for-A246259 row) col))
(definec (rowfun-for-A246259 row) (MATCHING-POS 1 1 (lambda (k) (= (- row 1) (A246271 k)))))
CROSSREFS
Transpose: A246258.
First row: A246261.
First column: A246280.
Sequence in context: A362978 A261147 A212952 * A105025 A129594 A214416
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Aug 22 2014
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)