A080900 -id:A080900 - cp's OEIS frontend

A080914 A080900 sorted and duplicates removed.

1, 6, 11, 16, 19, 21, 24, 29, 34, 37, 39, 42, 47, 52, 55, 57, 60, 63, 65, 66, 68, 71, 74, 76, 79, 84, 89, 92, 94, 97, 102, 107, 110, 112, 115, 118, 120, 121, 123, 126, 129, 131, 134, 139, 144, 147, 149, 152, 157, 162, 165, 167, 170, 173, 175, 176, 178

Offset: 1

N. J. A. Sloane, Apr 02 2003

nonn

Cf. A080900, A080919.

sort -n -u A080900

A080905 Sequence of run lengths in first differences of A080900.

Original entry on oeis.org

4, 1, 4, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 4, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 4, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 4, 1, 2, 1, 1, 1, 2

Offset: 1

N. J. A. Sloane, Apr 01 2003

nonn

Even after 400000 terms there is no clear pattern here.

			A080900 begins 1, 6, 11, 16, 21, 19, 24, 29, 34, 39, 37, 42, 47, 52, 57, 55, 60, 65, ..., the differences are 5, 5, 5, 5, -2, 5, 5, 5, 5, -2, ... with runs of lengths 4, 1, 4, 1, ...

Antti Karttunen, Table of n, a(n) for n = 1..102526

Cf. A080900, A080922, A080927.

up_to = 20000;
A080905list(up_to_n) = { my(xs=Map(), v, d, ds=vector(up_to_n)); mapput(xs,1,1); v = 1; for(n=2,1+up_to_n, v += (d=if(mapisdefined(xs,n), -2, +5)); mapput(xs,v,n); ds[n-1] = d); my(runlens=List([]), rl=1); for(i=2,#ds,if(ds[i]==ds[i-1],rl++, listput(runlens,rl);rl=1)); Vec(runlens); };
v080905 = A080905list(up_to);
A080905(n) = v080905[n]; \\ Antti Karttunen, Feb 24 2020

A080919 Numbers that do not appear in A080900.

Original entry on oeis.org

2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 20, 22, 23, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 38, 40, 41, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 67, 69, 70, 72, 73, 75, 77, 78, 80, 81, 82, 83, 85, 86, 87, 88, 90, 91, 93, 95, 96, 98, 99, 100, 101, 103, 104

Offset: 1

N. J. A. Sloane, Apr 04 2003

nonn

Complement of A080914.

A080912 a(n) = first number that appears n times in A080900.

Original entry on oeis.org

1, 523, 1277, 1277, 12694, 12694, 12692, 24154439, 186075352, 186074886

Offset: 1

N. J. A. Sloane, Apr 02 2003

Next term > 10^7. - Lambert Klasen (Lambert.Klasen(AT)gmx.net), Sep 26 2005
Next term > 26000000. - Lambert Herrgesell (zero815(AT)googlemail.com), Mar 09 2007
a(11) > 12*10^8. [Donovan Johnson, Sep 24 2009]

			Terms 181 through 200 of A080900 are: 502, 507, 512, 510, 515, 513, 518, 523, 521, 526, 531, 529, 527, 525, 523, 521, 519, 517, 522, 527 and at term 195 we see the first duplicate, 523. So a(2) = 523.

Cf. A080900, A080913 (when records occur).

One more term from Lambert Herrgesell (zero815(AT)googlemail.com), Mar 09 2007

a(9)-a(10) from Donovan Johnson, Sep 24 2009

A080913 Value of index in A080900 when a number first appears for the n-th time.

Original entry on oeis.org

1, 195, 525, 532, 6167, 6174, 6182, 12229008, 94219126, 94219751

Offset: 1

N. J. A. Sloane, Apr 02 2003

			Terms 181 through 200 of A080900 are 502 507 512 510 515 513 518 523 521 526 531 529 527 525 523 521 519 517 522 527 and at term 195 we see the first duplicate, 523. So a(2) = 195.

Cf. A080900, A080912 (actual records).

One more term from Lambert Herrgesell (zero815(AT)googlemail.com), Mar 09 2007

a(9)-a(10) from Donovan Johnson, Sep 24 2009

A080901 a(1)=2; for n>1, a(n)=a(n-1)-2 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

Original entry on oeis.org

2, 0, 5, 10, 8, 13, 18, 16, 21, 19, 24, 29, 27, 32, 37, 35, 40, 38, 36, 41, 39, 44, 49, 47, 52, 57, 55, 60, 58, 63, 68, 66, 71, 76, 74, 72, 70, 68, 66, 64, 62, 67, 72, 70, 75, 80, 78, 83, 81, 86, 91, 89, 94, 99, 97, 102, 100, 98, 103, 101, 106, 104, 102, 100

Offset: 1

N. J. A. Sloane and Benoit Cloitre, Apr 01 2003

Ivan Neretin, Table of n, a(n) for n = 1..1008
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.

Cf. A080578, A080900, A081745.

Fold[Append[#1, #1[[-1]] + If[MemberQ[#1, #2], -2, 5]] &, {2}, Range[2, 64]] (* Ivan Neretin, Mar 03 2016 *)

a(n)-n (n >= 1) (A081745) is periodic with period 168.

A080927 Where records occur in A080905 (endpoints of record runs).

Original entry on oeis.org

5, 198, 1281, 6162, 12749, 102883

Offset: 1

N. J. A. Sloane, Apr 04 2003

nonn

Cf. A080905, A080922, A080900.

A080922 Records in A080905.

Original entry on oeis.org

4, 7, 10, 21, 63, 81

Offset: 1

N. J. A. Sloane, Apr 04 2003

nonn

Cf. A080905, A080927, A080900.

A081746 a(1)=1; for n>1, a(n)=a(n-1)-3 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

Original entry on oeis.org

1, 6, 11, 16, 21, 18, 23, 28, 33, 38, 35, 40, 45, 50, 55, 52, 57, 54, 59, 64, 61, 66, 63, 68, 73, 78, 83, 80, 85, 90, 95, 100, 97, 102, 99, 104, 109, 106, 111, 108, 113, 118, 123, 128, 125, 130, 135, 140, 145, 142, 147, 144, 149, 146, 143, 148, 145, 150

Offset: 1

Benoit Cloitre, Apr 05 2003

Peter Munn, Table of n, a(n) for n = 1..5000
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.

Cf. A081747, A081748, A080578, A080900, A080901, A080939.

a[n_] := a[n] = If[n == 1, 1, If[MemberQ[Array[a, n-1], n], a[n-1] - 3, a[n-1] + 5]]; Array[a, 58] (* Jean-François Alcover, Oct 05 2018 *)

a(n) - n is periodic with period 648.

A080904 a(1)=1; for n>1, a(n)=a(n-1)-4 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

Original entry on oeis.org

1, 6, 11, 16, 21, 17, 22, 27, 32, 37, 33, 38, 43, 48, 53, 49, 45, 50, 55, 60, 56, 52, 57, 62, 67, 72, 68, 73, 78, 83, 88, 84, 80, 85, 90, 95, 91, 87, 92, 97, 102, 107, 103, 108, 104, 109, 114, 110, 106, 102, 107, 103, 99, 104, 100, 96, 92, 97, 102, 98, 103, 99

Offset: 1

Benoit Cloitre, Apr 01 2003

nonn

a(n)-n is eventually periodic with period 18. - Ivan Neretin, Mar 03 2016

Ivan Neretin, Table of n, a(n) for n = 1..1000
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.

Cf. A080578, A080900.

Fold[Append[#1, #1[[-1]] + If[MemberQ[#1, #2], -4, 5]] &, {1}, Range[2, 62]] (* Ivan Neretin, Mar 03 2016 *)

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A080914 A080900 sorted and duplicates removed.

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A080905 Sequence of run lengths in first differences of A080900.

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A080919 Numbers that do not appear in A080900.

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A080912 a(n) = first number that appears n times in A080900.

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A080913 Value of index in A080900 when a number first appears for the n-th time.

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A080901 a(1)=2; for n>1, a(n)=a(n-1)-2 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

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A080927 Where records occur in A080905 (endpoints of record runs).

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A080922 Records in A080905.

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A081746 a(1)=1; for n>1, a(n)=a(n-1)-3 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

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A080904 a(1)=1; for n>1, a(n)=a(n-1)-4 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

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