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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)