|
%I #21 Feb 25 2019 04:36:06
%S 4,9,10,15,16,35,36,39,40,77,78,91,92,93,94,119,120,133,134,141,142,
%T 161,162,175,176,177,178,261,262,341,342,345,346,355,356,407,408,411,
%U 412,451,452,473,474,475,476,517,518,539,540,543,548,583,584,595,596,597
%N a(1)=4. For n>=2, a(n) = smallest integer > a(n-1) that is not coprime to (n+1) but is coprime to n.
%C a(10^k): 4, 77, 1717, 46871, 1027767, 34696937, 1068983293, ... and a(2^k): 4, 9, 15, 39, 119, 345, 685, 2415, 5911, 18855, 47995, 124455, 290615, 794529, 2571825, 6910425, 18153749, 50986623, 147584275, 431488203, 1146090309, ..., . - _Robert G. Wilson v_, May 20 2008
%C Least term k such that there are just n consecutive terms: 4, 9, 91, 199068, 16621, 14052655, 17301, 6156769, 66781, 330484338, 376051, ???, 273222587, ???, 83335435, ..., . - _Robert G. Wilson v_, May 20 2008
%H Michael De Vlieger, <a href="/A139558/b139558.txt">Table of n, a(n) for n = 1..10000</a>
%p A139558 := proc(n) option remember ; local a,i; if n = 1 then RETURN(4) ; fi ; for a from A139558(n-1)+1 do if gcd(a,n) = 1 and gcd(a,n+1) <> 1 then RETURN(a) ; fi ; od: a ; end: seq(A139558(n),n=1..100) ; # _R. J. Mathar_, May 20 2008
%t f[1] = 4; f[n_] := f[n] = Block[{k = f[n - 1] + 1}, While[ GCD[n + 1, k] == 1 || GCD[n, k] > 1, k++ ]; k]; Array[f, 56] (* _Robert G. Wilson v_, May 20 2008 *)
%t FoldList[SelectFirst[Range[#1 + 1, #1 + 120], Function[k, And[CoprimeQ[k, #2], ! CoprimeQ[k, #2 + 1]]]] &, 4, Range[2, 56]] (* _Michael De Vlieger_, Oct 22 2017 *)
%Y Cf. A139557, A163643.
%K nonn
%O 1,1
%A _Leroy Quet_, Apr 27 2008
%E More terms from _R. J. Mathar_ and _Robert G. Wilson v_, May 20 2008
|
