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.

A162781 a(n) = A002410(n) - A162780(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1
Offset: 1

Views

Author

Omar E. Pol, Jul 13 2009

Keywords

Comments

This sequence is related to the Riemann zeta function.

Links

Crossrefs

Cf. A002410, A162774, A161914, A162780, A162782.

Extensions

More terms from Jinyuan Wang, Mar 02 2020

A161914 Gaps between the nontrivial zeros of Riemann zeta function, rounded to nearest integers, with a(1)=14.

Original entry on oeis.org

14, 7, 4, 5, 3, 5, 3, 2, 5, 2, 3, 3, 3, 1, 4, 2, 2, 3, 4, 1, 2, 4, 2, 3, 1, 4, 2, 1, 3, 2, 2, 2, 2, 4, 1, 2, 2, 3, 3, 2, 1, 3, 2, 2, 2, 1, 3, 2, 1, 2, 3, 1, 3, 1, 2, 3, 1, 1, 2, 2, 3, 2, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 1, 3, 1, 2, 1, 3, 2, 2, 2, 1, 2, 3, 2, 1, 3, 1, 2, 2, 2, 1, 2, 3, 1, 2, 1, 2, 1
Offset: 1

Views

Author

Omar E. Pol, Jun 26 2009

Keywords

Comments

We consider here the imaginary part of 1/2 + iy = z, for which Zeta(z) is a zero.
Note that these are not the first differences of A002410 because rounding is done here AFTER computing the differences. - R. J. Mathar, Jul 04 2009
What is the largest n such that a(n) > 0? - Charles R Greathouse IV, Jan 08 2012
This doesn't seem feasible to compute, probably more than 10^200. - Charles R Greathouse IV, Jan 29 2013

Examples

			The absolute difference between the first nontrivial zero (14.134725...) and the second nontrivial zero (21.022039...) is equal to 6.887314... which rounded to nearest integer is equal to 7, then a(2) = 7.

Links

Crossrefs

Cf. A002410, A162774, A162780-A162782, A208436, A210447, A221974.

Programs

  • Mathematica
    Join[{14}, Table[Round[Im[ZetaZero[n] - ZetaZero[n - 1]]], {n, 2, 100}]] (* Alonso del Arte, Jan 29 2013 *)
  • PARI
    diff(v)=vector(#v-1,i,v[i+1]-v[i])
concat(14, round(diff(lfunzeros(lzeta, 100)))) \\ Charles R Greathouse IV, Jul 26 2021

Extensions

Extended by R. J. Mathar, Jul 04 2009

A162782 a(n) = A162774(n) - A161914(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Omar E. Pol, Jul 13 2009

Keywords

Comments

This sequence is related to the Riemann zeta function.

Links

Crossrefs

Cf. A002410, A162774, A161914, A162780, A162781.

Extensions

More terms (cf. raw data table linked in A161914) from Hagen von Eitzen, Oct 03 2009
More terms from Jinyuan Wang, Mar 14 2020

A162774 14 together with the first differences of A002410.

Original entry on oeis.org

14, 7, 4, 5, 3, 5, 3, 2, 5, 2, 3, 3, 3, 2, 4, 2, 3, 2, 4, 1, 2, 4, 2, 2, 2, 3, 3, 1, 3, 2, 3, 1, 2, 4, 1, 2, 2, 3, 2, 2, 1, 4, 2, 1, 2, 2, 3, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 1, 2, 2, 3, 1, 2, 1, 3, 2, 1, 2, 2, 2, 3, 1, 1, 2, 3, 1, 2, 2, 1, 3, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 2, 0, 3, 1, 2, 2, 2, 1, 2, 3, 1, 2, 1, 2, 1, 3
Offset: 1

Views

Author

Omar E. Pol, Jul 13 2009

Keywords

Comments

This sequence is related to the Riemann zeta function (very similar to A161914).
All but finitely many terms of this sequence are 0. What is the largest n such that a(n) > 0? - Charles R Greathouse IV, Jul 16 2012

Links

Crossrefs

Cf. A002410, A161914, A162780, A162781, A162782.

Extensions

More terms (data table at A161914) from Hagen von Eitzen, Oct 03 2009
a(92)-a(105) corrected by Omar E. Pol, Oct 08 2009
Missing a(92)=0 inserted by Sean A. Irvine, Mar 03 2023
Showing 1-4 of 4 results.

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