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A090937 a(1) = 1, a(2) = 2; for n > 2, a(n) = a(n-1) + (smallest integer >= n which is coprime to a(n-1)). 1
1, 2, 5, 9, 14, 23, 30, 41, 50, 61, 72, 85, 98, 113, 128, 145, 162, 181, 200, 221, 242, 265, 288, 313, 338, 365, 392, 421, 450, 481, 512, 545, 578, 613, 648, 685, 722, 761, 800, 841, 882, 925, 968, 1013, 1058, 1105, 1152, 1201, 1250, 1301, 1352, 1405, 1458 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

a(2*n-1) = 2*n^2, a(2*n) = 2*n^2 + 2*n + 1, for n > 4.

From Wesley Ivan Hurt, Aug 03 2015: (Start)

G.f.: x*(1+x^2+x^3-x^4+3*x^5-3*x^6-2*x^9+2*x^10)/((1-x)^3*(1+x)).

a(n) = ceiling((n+1)^2/2) = A000982(n+1), for n > 7. (End)

MAPLE

A090937:=n->(2*n^2+4*n+3+(-1)^n)/4: (1, 2, 5, 9, 14, 23, 30, seq(A090937(n), n=8..100)); # Wesley Ivan Hurt, Aug 03 2015

MATHEMATICA

lst = {}; a = 2; Do[d = n; While[! CoprimeQ[a, d], d++]; a = a + d; AppendTo[lst, a], {n, 3, 53}]; Join[{1, 2}, lst] (* Arkadiusz Wesolowski, Jun 03 2013 *)

nxt[{n_, a_}]:=Module[{k=n+1}, While[!CoprimeQ[a, k], k++]; {n+1, a+k}]; Join[ {1}, Transpose[NestList[nxt, {2, 2}, 60]][[2]]] (* Harvey P. Dale, Apr 07 2015 *)

CoefficientList[Series[(1+x^2+x^3-x^4+3x^5-3x^6-2x^9+2x^10)/((1-x)^3*(1+ x)), {x, 0, 50}], x] (* or *) Join[{1, 2, 5, 9, 14, 23, 30}, Table[(2n^2 +4n + 3 +(-1)^n)/4, {n, 8, 100}]] (* Wesley Ivan Hurt, Aug 03 2015 *)

PROG

(PARI) my(x='x+O('x^60)); Vec(x*(1+x^2+x^3-x^4+3*x^5-3*x^6-2*x^9+2*x^10 )/((1-x)^3*(1+x))) \\ G. C. Greubel, Feb 04 2019

(MAGMA) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( x*(1+x^2+x^3-x^4+3*x^5-3*x^6-2*x^9+2*x^10 )/((1-x)^3*(1+x)) )); // G. C. Greubel, Feb 04 2019

(Sage) a=(x*(1+x^2+x^3-x^4+3*x^5-3*x^6-2*x^9+2*x^10 )/((1-x)^3*(1+x)) ).series(x, 60).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 04 2019

(GAP) Concatenation([1, 2, 5, 9, 14, 23, 30], List([8..60], n -> (2*n^2 +4*n +3 +(-1)^n)/4)); # G. C. Greubel, Feb 04 2019

CROSSREFS

Cf. A000982.

Sequence in context: A098065 A123690 A199935 * A338666 A325717 A291942

Adjacent sequences:  A090934 A090935 A090936 * A090938 A090939 A090940

KEYWORD

easy,nonn

AUTHOR

Amarnath Murthy, Dec 29 2003

EXTENSIONS

Name changed and sequence extended by Arkadiusz Wesolowski, Jun 03 2013

STATUS

approved

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Last modified January 26 20:02 EST 2022. Contains 350599 sequences. (Running on oeis4.)