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.

Showing 1-4 of 4 results.

A080023 log_phi(n) is closer to an integer than is log_phi(m) for any m with 2<=m

Original entry on oeis.org

2, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521
Offset: 1

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Author

Dean Hickerson, Jan 20 2003

Keywords

Comments

This is the sequence of Lucas numbers (A000032) without the term 1.

Examples

			log_phi(2) = 1+0.440..., log_phi(3) = 2+0.283..., log_phi(4) = 3-0.119..., log_phi(7) = 4+0.0437...

References

Crossrefs

Cf. A000032, A080021, A080022.

Programs

  • PARI
    lista(nn) = {flmin = 1; phi = (1 + sqrt(5))/2; for (i = 2, nn, li = log(i)/log(phi); fli = abs(round(li) - li); if (fli < flmin, print1(i, ", "); flmin = fli;););} \\ Michel Marcus, Aug 29 2013

A080022 Numbers n such that log_pi(n) is closer to an integer than is log_pi(m) for any m with 2<=m

Original entry on oeis.org

2, 3, 10, 31, 306, 9488, 9489, 29808, 29809, 93648, 294204, 9122171, 28658146, 888582403, 8769956796, 27551631843, 86556004192, 854273519914, 2683779414318, 8431341691876, 26487841119103, 26487841119104
Offset: 1

Views

Author

Dean Hickerson, Jan 20 2003

Keywords

Comments

Every term is floor(pi^k)+r for some integers k and r with k>=1 and -1 <= r <= 1.

Examples

			log_pi(2) = 1-0.394..., log_pi(3) = 1-0.0402..., log_pi(10) = 2+0.0114..., log_pi(31) = 3-0.000176...

References

Crossrefs

Cf. A080021, A080023.

Programs

  • PARI
    lista(nn) = {flmin = 1; for (i = 2, nn, li = log(i)/log(Pi); fli = abs(round(li) - li); if (fli < flmin, print1(i, ", "); flmin = fli;););} \\ Michel Marcus, Aug 29 2013

A079663 Sequence of the radicands that give the best radical approach to e.

Original entry on oeis.org

1, 2, 3, 6, 7, 19, 20, 148, 403, 1096, 1097, 2980, 2981, 8103, 59874, 162755, 1202603, 1202604, 3269017, 8886110, 8886111, 24154952, 24154953, 65659969, 178482301, 3584912846, 9744803446, 26489122130, 72004899337, 195729609428
Offset: 1

Views

Author

Carlos Alves, Jan 24 2003

Keywords

Comments

Numbers n such that n^(1/m) is closer to e than for previous n. m is given by the Floor/Ceiling of Log[n].
Each group of entries exceed the previous group by e^k where k is an integer.

Examples

			e-1^1 > e-2^1 > 3^1-e > e-6^(1/2) > e-7^(1/2) > e-19^(1/3) > e-20^(1/3) > ...

Crossrefs

Cf. A004791, A080021.

Programs

  • Mathematica
    ls = {}; mx = 1; Do[mn = Min[Abs[{n^(1/Floor[Log[n]]) - E, E - n^(1/Ceiling[Log[n]])}]]; If[mn < mx, mx = mn; AppendTo[ls, {n, mx}]], {n, 3, 500000}]; N[ls] // TableForm

Extensions

Edited and extended by Robert G. Wilson v, Jan 24 2003

A345328 a(n) is the smallest integer k>1 such that |log(k)-round(log(k))| is smaller than 10^(-n).

Original entry on oeis.org

3, 20, 1096, 2981, 59874, 442413, 8886110, 65659969, 178482301, 3584912846, 26489122130, 195729609429, 3931334297144, 78962960182680, 214643579785916, 4311231547115195, 31855931757113756, 86593400423993747, 12851600114359308275, 34934271057485095348
Offset: 1

Views

Author

Andrzej Kukla, Jun 14 2021

Keywords

Comments

In other words, a(n) is the smallest integer k>1 such that the distance between log(k) and nearest integer to log(k) is smaller than 10^(-n).

Examples

			For n=4 a(n)=2981, because 2981 is the smallest integer greater than 1 such that |log(2981)-round(2981)| = 0.00001409... < 10^(-4).

Crossrefs

Cf. A000193, A000227, A079663, A080021.

Programs

  • Maple
    n := 1: for i from 2 to 10^10 do if abs(evalf(log(i)) - floor(log(i) + 1/2)) < 10^(-n) then print(i); n := n + 1 fi end do;
  • PARI
    \\ suitable precision needed.
a(n)={my(epsilon=1.0/10^n); for(k=1, oo, my(t=floor(exp(k))); if(k-log(t)Andrew Howroyd, Jun 14 2021

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jun 14 2021
Showing 1-4 of 4 results.

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