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

1,1

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

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 *)

Crossrefs

Cf. A139557, A163643.

Sequence in context: A064973 A133764 A163643 * A219556 A110602 A254923

Adjacent sequences: A139555 A139556 A139557 * A139559 A139560 A139561

Keyword

nonn

Author

Leroy Quet, Apr 27 2008

Extensions

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

Status

approved