

A133256


a(4*n+1) = 4*n+1, a(4*n+2) = 4*n+2, a(4*n+3) = 4*n+4, a(4*n+4) = 4*n+3.


3



1, 2, 4, 3, 5, 6, 8, 7, 9, 10, 12, 11, 13, 14, 16, 15, 17, 18, 20, 19, 21, 22, 24, 23, 25, 26, 28, 27, 29, 30, 32, 31, 33, 34, 36, 35, 37, 38, 40, 39, 41, 42, 44, 43, 45, 46, 48, 47, 49, 50, 52, 51, 53, 54, 56, 55, 57, 58, 60, 59, 61, 62, 64, 63, 65, 66, 68, 67, 69, 70, 72, 71
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OFFSET

1,2


COMMENTS

A permutation of the positive integers, swapping consecutive values congruent to 3 and 4 (mod 4).  Franklin T. AdamsWatters, Jan 22 2012.
This is the lexicographically earliest sequence of distinct positive integers such that no polynomial of degree d can be fitted to d+2 consecutive terms (equivalently, such that no iterated difference is zero).  Pontus von Brömssen, Dec 26 2021


LINKS



FORMULA

a(n) = a(n1) + a(n4)  a(n5) for n > 5.
G.f.: x*(x^4  x^3 + 2*x^2 + x + 1)/(x^5  x^4  x + 1). (End)
Sum_{n>=1} (1)^(n+1)/a(n) = Pi/4  log(2)/2.  Amiram Eldar, Jan 31 2023


MATHEMATICA

Table[Which[Mod[n, 4]==3, n+1, Divisible[n, 4], n1, True, n], {n, 40}] (* or *) Partition[Range[40], 4]/.{a_, b_, c_, d_}>{a, b, d, c}//Flatten (* Harvey P. Dale, Aug 29 2016 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



