A079000 -id:A079000 - cp's OEIS frontend

A080724 a(0) = 2; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 1 mod 3".

2, 3, 4, 7, 10, 11, 12, 13, 14, 15, 16, 19, 22, 25, 28, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset: 0

N. J. A. Sloane, Mar 08 2003

Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

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 (math.NT/0305308)
Index entries for sequences of the a(a(n)) = 2n family

Cf. A079000, A080720, ...

{a=2; m=[2]; for(n=1,66,print1(a,","); a=a+1; if(a%3==1&&a==n,qwqw=qwqw,if(m==[], while(a%3!=1&&a==n,a++),if(m[1]==n, while(a%3!=1,a++); m=if(length(m) == 1,[],vecextract(m,"2..")),if(a%3==1,a++))); m=concat(m,a)))}

a(a(n)) = 3*n+4, n >= 0.

More terms and PARI code from Klaus Brockhaus, Mar 08 2003

A080725 a(1) = 2; for n>1, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 1 mod 3".

Original entry on oeis.org

2, 4, 5, 7, 10, 11, 13, 14, 15, 16, 19, 20, 22, 25, 28, 31, 32, 33, 34, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 55, 58, 59, 60, 61, 64, 65, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 106, 109, 112, 113, 114, 115, 118, 119, 121

Offset: 1

N. J. A. Sloane, Mar 08 2003

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 (math.NT/0305308)
Index entries for sequences of the a(a(n)) = 2n family

Cf. A079000, A080720, ...

{a=2; m=[2]; for(n=2,68,print1(a,","); a=a+1; if(m[1]==n, while(a%3!=1,a++); m=if(length(m)==1,[],vecextract(m,"2..")),if(a%3==1,a++)); m=concat(m,a))}

a(a(n)) = 3*n+1, n >= 1.

More terms and PARI code from Klaus Brockhaus, Mar 08 2003

A080726 a(0) = 0; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 2 mod 3".

Original entry on oeis.org

0, 3, 4, 5, 8, 11, 12, 13, 14, 15, 16, 17, 20, 23, 26, 29, 32, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset: 0

N. J. A. Sloane, Mar 08 2003

Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

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 (math.NT/0305308)
Index entries for sequences of the a(a(n)) = 2n family

Cf. A079000, A080720, ...

{a=0; m=[]; for(n=1,66,print1(a,","); a=a+1; if(a%3==2&&a==n,qwqw=qwqw,if(m==[], while((a%3!=2&&a==n)||a%3==2,a++),if(m[1]==n, while(a%3!=2,a++); m=if(length(m)==1,[],vecextract(m,"2..")),if(a%3==2,a++))); m=concat(m,a)))}

a(a(n)) = 3*n+2, n >= 1.

More terms and PARI code from Klaus Brockhaus, Mar 09 2003

A080727 a(0) = 1; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 2 mod 3".

Original entry on oeis.org

1, 2, 5, 6, 7, 8, 11, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122

Offset: 0

N. J. A. Sloane, Mar 08 2003

Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

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 (math.NT/0305308)
Index entries for sequences of the a(a(n)) = 2n family

Cf. A079000, A080720, ...

{a=1; m=[]; for(n=1,69,print1(a,","); a=a+1; if(a%3==2&&a==n,qwqw=qwqw,if(m==[], while(a%3!=2&&a==n,a++),if(m[1]==n, while(a%3!=2,a++); m=if(length(m)==1,[],vecextract(m,"2..")),if(a%3==2,a++))); m=concat(m,a)))}

a(a(n)) = 3*n+2, n >= 0.

More terms and PARI code from Klaus Brockhaus, Mar 09 2003

A080728 a(0) = 3; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 2 mod 3".

Original entry on oeis.org

3, 4, 6, 8, 11, 12, 14, 15, 17, 18, 19, 20, 23, 24, 26, 29, 30, 32, 35, 38, 41, 42, 43, 44, 47, 48, 50, 51, 52, 53, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 71, 74, 77, 78, 79, 80, 83, 84, 86, 89, 92, 95, 96, 97, 98, 101, 102, 104, 107, 110, 113, 116, 119, 122, 125, 128

Offset: 0

N. J. A. Sloane, Mar 08 2003

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 (math.NT/0305308)
Index entries for sequences of the a(a(n)) = 2n family

Cf. A079000, A080720, ...

{a=3; m=[3]; for(n=1,68,print1(a,","); a=a+1; if(a%3==2&&a==n,qwqw=qwqw,if(m==[], while((a%3!=2&&a==n)||a%3==2,a++),if(m[1]==n, while(a%3!=2,a++); m=if(length(m)==1,[],vecextract(m,"2..")),if(a%3==2,a++))); m=concat(m,a)))}

a(a(n)) = 3*n+8, n >= 0.

More terms and PARI code from Klaus Brockhaus, Mar 09 2003

A080780 a(1)=2; for n > 1, a(n) is the smallest integer greater than a(n-1) consistent with the condition "n is in the sequence if and only if a(n) is congruent to 0 (mod 6)".

Original entry on oeis.org

2, 6, 7, 8, 9, 12, 18, 24, 30, 31, 32, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 60, 66, 67, 68, 69, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150

Offset: 1

Benoit Cloitre, Feb 23 2003

nonn

J.-P. Allouche, N. Rampersad and J. Shallit, On integer sequences whose first iterates are linear, Aequationes Math. 69 (2005), 114-127

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 (math.NT/0305308)
Index entries for sequences of the a(a(n)) = 2n family

Cf. A079000.

A081261 Start with a(1)=4; apply 4 -> 665, 5 -> 56665, 6 -> 566665; iterate.

Original entry on oeis.org

4, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 5, 5, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 5, 5, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 5, 5, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6

Offset: 1

Matthew Vandermast, Mar 14 2003

a(n)= A081260(n) - A081260(n-1) (taking A081260(0) as equal to 0). Sum of first n terms = A081260(n).

			4 -> 665 -> 56666556666556665 -> ...

Cf. A079000, A079948.

A242940 a(n) is the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a term of the sequence if and only if a(n) is a Fibonacci number".

Original entry on oeis.org

1, 2, 3, 6, 7, 8, 13, 21, 22, 23, 24, 25, 34, 35, 36, 37, 38, 39, 40, 41, 55, 89, 144, 233, 377, 378, 379, 380, 381, 382, 383, 384, 610, 987, 1597

Offset: 1

J. Lowell, Jun 12 2014

			a(4) cannot be 5 because that would require 4 to be a term of this sequence.

Cf. A079000, A079253, A079254, A079258, A079256, A079257.

cp's OEIS Frontend

A080724 a(0) = 2; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 1 mod 3".

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A080725 a(1) = 2; for n>1, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 1 mod 3".

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A080726 a(0) = 0; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 2 mod 3".

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Programs

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A080727 a(0) = 1; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 2 mod 3".

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Author

Keywords

References

Links

Crossrefs

Programs

PARI

Formula

Extensions

A080728 a(0) = 3; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 2 mod 3".

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

Extensions

A080780 a(1)=2; for n > 1, a(n) is the smallest integer greater than a(n-1) consistent with the condition "n is in the sequence if and only if a(n) is congruent to 0 (mod 6)".

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Author

Keywords

References

Links

Crossrefs

A081261 Start with a(1)=4; apply 4 -> 665, 5 -> 56665, 6 -> 566665; iterate.

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A242940 a(n) is the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a term of the sequence if and only if a(n) is a Fibonacci number".

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