A139558 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.

4, 9, 10, 15, 16, 35, 36, 39, 40, 77, 78, 91, 92, 93, 94, 119, 120, 133, 134, 141, 142, 161, 162, 175, 176, 177, 178, 261, 262, 341, 342, 345, 346, 355, 356, 407, 408, 411, 412, 451, 452, 473, 474, 475, 476, 517, 518, 539, 540, 543, 548, 583, 584, 595, 596, 597

Offset: 1

Author

Leroy Quet, Apr 27 2008

Keywords

• nonn

Comments

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

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A139557, A163643.

Programs

Maple

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

Mathematica

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 *)
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 *)

Extensions

More terms from R. J. Mathar and Robert G. Wilson v, May 20 2008