cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 71-80 of 88 results. Next

A379050 a(n) = b(b(n)), where b(k) = A121053(k).

Original entry on oeis.org

1, 3, 5, 7, 2, 11, 13, 19, 23, 17, 37, 41, 29, 53, 67, 31, 73, 89, 43, 103, 107, 47, 127, 139, 59, 163, 61, 167, 71, 191, 197, 211, 79, 229, 83, 241, 97, 263, 283, 101, 307, 313, 109, 331, 347, 113, 353, 401, 131, 419, 137, 439, 149, 443, 479, 151, 487, 157, 509, 541, 173, 563, 577, 179, 601, 181, 607, 643, 193, 647, 199, 661, 673, 727, 223, 761, 227, 787, 233, 797, 821, 239
Offset: 1

Views

Author

N. J. A. Sloane, Dec 14 2024

Keywords

Comments

Suggested by the formula a(a(n)) = 2*n + 3 for the analogous sequence A079000.

Links

Crossrefs

Cf. A079000, A121053.

Programs

  • Mathematica
    nn = 2^8; a[1] = 2; u = 4; v = {1}; w = {2}; p = 3;
Do[If[MemberQ[w, n], k = p;
  w = Append[DeleteCases[w, n], p]; p = NextPrime[p],
  If[Length[v] == 0,
    k = u; AppendTo[w, u],
    k = First[v]; v = Rest[v]]];
  Set[{a[n]}, {k}];
  If[n + 1 >= u, u++; While[PrimeQ[u], u++]], {n, 2, nn}];
{1}~Join~TakeWhile[Array[a[a[#]] &, nn], IntegerQ] (* Michael De Vlieger, Dec 17 2024 *)

A080038 Start with a(1)=3; apply 3 -> 343, 4 -> 3443; iterate.

Original entry on oeis.org

3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4
Offset: 1

Views

Author

Matthew Vandermast, Mar 14 2003

Keywords

Comments

a(n)= A080753(n+1) - A080753(n). Sum of first n terms + 2 = A080753(n).

Examples

			3 -> 343 -> 3433443343 -> ...

Crossrefs

Cf. A079000, A079948.

Programs

  • Mathematica
    SubstitutionSystem[{3->{3,4,3},4->{3,4,4,3}},{3},{5}][[1]] (* Harvey P. Dale, Jan 01 2024 *)

A080633 a(1)=3; 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 1 (mod 4)".

Original entry on oeis.org

3, 4, 5, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 29, 33, 37, 41, 45, 49, 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, 81, 82, 83, 84, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141
Offset: 1

Views

Author

Benoit Cloitre, Feb 23 2003

Keywords

Comments

Equivalently: unique monotonic sequence satisfying a(1)=3, a(a(n))=4n+1.

Links

Formula

There is an explicit formula for a(n) similar to that for A079000.

Extensions

More terms from Matthew Vandermast, Mar 13 2003

A080641 a(1) = 4; for n>1, a(n) is taken to be the smallest 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) is divisible by 5".

Original entry on oeis.org

4, 6, 7, 10, 11, 15, 20, 21, 22, 25, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 45, 50, 51, 52, 55, 56, 57, 58, 59, 60, 65, 70, 75, 76, 80, 85, 90, 95, 100, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 120, 125, 126, 127, 130, 135, 140, 145, 150, 155, 156, 157
Offset: 1

Views

Author

N. J. A. Sloane and Benoit Cloitre, Feb 28 2003

Keywords

Links

Crossrefs

Cf. A080639, A080640, A079000.

Formula

{a(a(n))} = {5i, i >= 2}.

Extensions

More terms from Matthew Vandermast, Feb 28 2003

A080644 a(1) = 5; for n>1, a(n) is taken to be the smallest 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) is divisible by 6".

Original entry on oeis.org

5, 7, 8, 9, 12, 13, 18, 24, 30, 31, 32, 36, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 66, 72, 73, 74, 75, 78, 79, 80, 81, 82, 83, 84, 90, 96, 102, 108, 109, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 187, 188, 189, 190
Offset: 1

Views

Author

N. J. A. Sloane and Benoit Cloitre, Feb 28 2003

Keywords

Links

Crossrefs

Cf. A080639, A080640, A079000.

Formula

{a(a(n))} = {6i, i >= 2}.

Extensions

More terms from Matthew Vandermast, Mar 13 2003

A080645 a(1) = 1; for n>1, a(n) is taken to be the smallest integer greater than a(n-1) which is consistent with the condition "for n>1, if n is a member of the sequence then a(n) is even".

Original entry on oeis.org

1, 2, 4, 6, 7, 8, 10, 12, 13, 14, 15, 16, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 38, 40, 42, 44, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107
Offset: 1

Views

Author

N. J. A. Sloane and Benoit Cloitre, Feb 28 2003

Keywords

References

  • 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

Links

Crossrefs

Cf. A080639, A080640, A079000.
Essentially the same as A007378.

Formula

a(1)=1, a(2)=2, a(3)=4; then for k>=1, abs(j)<=2^k: a(3*2^k+j)=4*2^k+3/2*j+abs(j)/2.
{a(a(n))} = {1, 2, 2i, i >= 3}.

A080646 a(1) = 3; for n>1, a(n) is taken to be the smallest integer greater than a(n-1) which is consistent with the condition "if n is a member of the sequence then a(n) is divisible by 3".

Original entry on oeis.org

3, 4, 8, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 28, 32, 36, 40, 44, 48, 52, 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, 81, 82, 83, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168
Offset: 1

Views

Author

Benoit Cloitre, Feb 12 2003

Keywords

Links

Crossrefs

Cf. A080639, A080640, A079000.

Formula

For k>=2 and i=0, ..., 4^k/2, a((4/3)*(4^(k-1)-1) + i) = (5*4^k-8)/6 + i, a((5*4^k-8)/6 + i) = (4/3)*(4^k-1) + 4*i. - N. J. A. Sloane, Mar 02 2003
{a(a(n))} = {4i, i >= 2}.

A080714 a(n) is taken to be the (n-th)-smallest positive integer greater than a(n-1) that is consistent with the condition "n is a member of the sequence if and only if a(n) is odd.".

Original entry on oeis.org

1, 6, 12, 20, 30, 41, 54, 70, 88, 108, 130, 153, 178, 206, 236, 268, 302, 338, 376, 415, 456, 500, 546, 594, 644, 696, 750, 806, 864, 923, 984, 1048, 1114, 1182, 1252, 1324, 1398, 1474, 1552, 1632, 1713, 1796, 1882, 1970, 2060, 2152, 2246, 2342, 2440, 2540
Offset: 1

Views

Author

Matthew Vandermast, Mar 05 2003

Keywords

Examples

			a(2) cannot be 2 because that would require the second term to be odd, a condition 2 does not satisfy. Since 2 is therefore not in the sequence, the second term must be even. The second-smallest even number greater than 2 is 6; therefore a(2) is 6.

Links

Crossrefs

Cf. A079000.

A080722 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 term of the sequence if and only if a(n) == 1 (mod 3)".

Original entry on oeis.org

0, 1, 3, 4, 7, 8, 9, 10, 13, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 34, 37, 40, 43, 46, 49, 52, 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, 81, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121
Offset: 0

Views

Author

N. J. A. Sloane, Mar 08 2003

Keywords

Links

Crossrefs

Cf. A079000, A080720.

Programs

  • PARI
    {a=0; m=[]; for(n=1,70,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)))} \\ Klaus Brockhaus, Mar 08 2003

Formula

a(a(n)) = 3*n-2, n >= 2.

Extensions

More terms from Klaus Brockhaus, Mar 08 2003

A080723 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) == 1 mod 3".

Original entry on oeis.org

1, 4, 5, 6, 7, 10, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 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, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124
Offset: 0

Views

Author

N. J. A. Sloane, Mar 08 2003

Keywords

References

  • 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

Links

Crossrefs

Cf. A079000, A080720, ...

Programs

  • PARI
    {print1(1,","); a=4; m=[4]; 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))}

Formula

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

Extensions

More terms and PARI code from Klaus Brockhaus, Mar 08 2003
Previous Showing 71-80 of 88 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.