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.

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A330360 First occurrence of run of lucky numbers congruent to 1 mod 4 of exactly length n.

Original entry on oeis.org

1, 9, 285, 933, 741, 11173, 15109, 33705, 100737, 24025, 34197, 86829, 5370693, 6457761, 2287341, 26529033, 53099457, 770289, 754577025, 256655365, 765951429, 2618761237, 1075872265, 2405972445, 2767592133
Offset: 1

Views

Author

Amiram Eldar, Dec 12 2019

Keywords

Comments

Calculated using Hugo van der Sanden's Lucky numbers up to 10^9 (private communication).
a(20) = 256655365.
a(26) > 4*10^9. - Giovanni Resta, May 10 2020

Examples

			a(1) = 1 since 1 is the first lucky number congruent to 1 mod 4, and the next lucky number is 3 which is not congruent to 1 mod 4.
a(2) = 9 since 9 and 13 are 2 consecutive lucky numbers congruent to 1 mod 4, following 7 and followed by 15 which are both not congruent to 1 mod 4.

Links

Crossrefs

Cf. A000959, A055623, A137168, A330359, A330361.

Extensions

a(19)-a(25) from Giovanni Resta, May 10 2020

A330359 Race of lucky numbers of the form 4*k - 1 vs. 4*k + 1 is tied at the a(n)-th lucky number.

Original entry on oeis.org

2, 4, 6, 16, 20, 22, 24, 2684, 2686, 2688, 2696, 2710, 2712, 109978, 110026, 110028, 110030, 110052, 110056, 110060, 110068, 110070, 110154, 110156, 110158, 110160, 118048, 118050, 118126, 118128, 118130, 118132, 118134, 118136, 118138, 118152, 118154, 118156
Offset: 1

Views

Author

Amiram Eldar, Dec 12 2019

Keywords

Comments

All the terms are even by definition. For each term m, there are m/2 lucky numbers of the form 4*k - 1 and m/2 lucky numbers of the form 4*k + 1 up to the m-th lucky number.
Gardiner et al. (1956) noted that the ratio between the numbers of lucky numbers of the form 4*k - 1 and 4*k + 1 seems to tend to 1, with a preponderance, at first, of the lucky numbers of the form 4*k + 3.

Examples

			6 is in the sequence since the first 6 lucky numbers are 1, 3, 7, 9, 13, 15, half of them are of the form 4*k-1 (3, 7, 15) and half of the form 4*k+1 (1, 9, 13).

Links

Crossrefs

Cf. A000959, A038691, A137168, A137170, A330360, A330361.

Programs

  • Mathematica
    lucky = Import["b000959.txt", "Table"][[;; , 2]]; Flatten[Position[Accumulate[ Mod[lucky, 4] - 2], 0]] (* use the b-file from A000959 *)
Showing 1-2 of 2 results.

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

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