A217662 -id:A217662 - cp's OEIS frontend

A217663 a(n) = A217662(n+2)/A217662(n) - 1, n > 0.

1, 3, 1, 5, 3, 7, 1, 3, 5, 11, 1, 13, 7, 5, 1, 17, 3, 19, 5, 1, 11, 23, 1, 5, 13, 1, 1, 29, 5, 31, 1, 11, 17, 1, 1, 37, 19, 13, 1, 41, 1, 43, 11, 1, 23, 47, 1, 1, 5, 17, 13, 53, 1, 1, 1, 1, 29, 59, 1, 61, 31, 1, 1, 13, 11, 67, 17, 23, 1, 71, 1, 73, 37, 1, 1

Offset: 1

Pedja Terzic, Oct 10 2012

nonn

a(prime(n)-1) = prime(n) for n>1, so this sequence includes all odd primes. - Jon Perry, Oct 10 2012, edited & corrected by M. F. Hasler, Oct 11 2012

Cf. A135504, A217662.

RecurrenceTable[{a[n]==a[n-2]+LCM[n-1,a[n-2]],a[1]==2,a[2]==2},a{n,3,51}] /RecurrenceTable[{a[n]==a[n-2]+LCM[n-1,a[n-2]],a[1]==2,a[2]==2},a,{n,1,49}]-1
t = {2, 2}; Do[AppendTo[t, t[[-2]] + LCM[n - 1, t[[-2]]]], {n, 3, 100}]; Drop[t, 2]/Drop[t, -2] - 1 (* T. D. Noe, Oct 10 2012 *)

A304821 For n > 3, a(n) = a(n-3) + lcm(a(n-3), n-2) with a(1)=6, a(2)=6, a(3)=6.

Original entry on oeis.org

6, 6, 6, 12, 12, 18, 72, 24, 144, 144, 96, 864, 1728, 192, 12096, 13824, 1152, 24192, 248832, 2304, 483840, 1492992, 18432, 5806080, 35831808, 36864, 34836480, 501645312, 147456, 69672960, 15049359360, 884736

Offset: 1

Pedja Terzic, May 19 2018

nonn

Cf. A135504, A217662.

Fold[Append[#1, #1[[-3]] + LCM[#1[[-3]], #2 + 1]] &, {6, 6, 6}, Range@ 29] (* Michael De Vlieger, May 20 2018 *)

Recurrence(n)={b1=6;b2=6;b3=6;list=[6,6,6];for(k=4,n,b4=b1+lcm(k-2,b1);list=concat(list,b4);b1=b2;b2=b3;b3=b4);print(list)}

A304822 a(n) = A304821(n+3)/A304821(n) - 1.

Original entry on oeis.org

1, 1, 2, 5, 1, 7, 1, 3, 5, 11, 1, 13, 7, 5, 1, 17, 1, 19, 5, 7, 11, 23, 1, 5, 13, 3, 1, 29, 5, 31, 1, 11, 17, 1, 1, 37, 19, 13, 1, 41, 1, 43, 11, 5, 23, 47, 1, 7, 1, 17, 13, 53, 1, 1, 1, 19, 29, 59, 1, 61, 31, 1, 1, 13, 11, 67, 17, 23, 1, 71, 1, 73

Offset: 1

Pedja Terzic, May 19 2018

nonn

Conjecture: This sequence consists of 1's and primes only.

a(n) divides n+1. - A.H.M. Smeets, Jul 02 2018

A.H.M. Smeets, Table of n, a(n) for n = 1..20000

Cf. A135504, A217662, A217663, A304821.

Drop[#, 3] &@ Fold[Append[#1, {#2, #2/#1 - 1} & @@ {#1[[-3, 1]], #1[[-3, 1]] + LCM[#1[[-3, 1]], #2 + 1]}] &, {{6, 0}, {6, 0}, {6, 0}}, Range@ 72] [[All, -1]] (* Michael De Vlieger, May 20 2018 *)

Generator(n)={b1=6;b2=6;b3=6;list=[];for(k=4,n,b4=b1+lcm(k-2,b1);a=b4/b1-1;list=concat(list,a);b1=b2;b2=b3;b3=b4);print(list)}

from math import gcd
n,an0,an1,an2 = 3,6,6,6
while n-3 < 200:
    n += 1
    an0,an1,an2,an3 = an2+an2*(n-2)//gcd(an2,n-2),an0,an1,an2
    # an0 = A304821(n), an3 = A304821(n-3)
    print(n-3,an0//an3-1)
# A.H.M. Smeets, Jul 02 2018

cp's OEIS Frontend

A217663 a(n) = A217662(n+2)/A217662(n) - 1, n > 0.

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A304821 For n > 3, a(n) = a(n-3) + lcm(a(n-3), n-2) with a(1)=6, a(2)=6, a(3)=6.

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A304822 a(n) = A304821(n+3)/A304821(n) - 1.

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