The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Robert Price (See also Robert Price's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A376470

Numbers k such that (29^k - 2^k)/27 is prime.
(history; published version)

#3 by Robert Price at Tue Sep 24 00:13:31 EDT 2024

STATUS

editing

proposed

#2 by Robert Price at Tue Sep 24 00:12:48 EDT 2024

NAME

allocated for Robert Price

Numbers k such that (29^k - 2^k)/27 is prime.

DATA

2, 7, 139, 983, 3257, 10181, 26387, 36187, 42557

OFFSET

1,1

COMMENTS

The definition implies that k must be a prime.

a(10) > 10^5.

LINKS

P. Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>.

J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

H. Dubner and T. Granlund, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/DUBNER/dubner.html">Primes of the Form (b^n+1)/(b+1)</a>, J. Integer Sequences, 3 (2000), #P00.2.7.

H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>.

MATHEMATICA

Select[Prime[Range[1000]], PrimeQ[(29^# - 2^#)/27] &]

CROSSREFS

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236.

KEYWORD

allocated

nonn,hard,more,new

AUTHOR

Robert Price, Sep 24 2024

STATUS

approved

editing

#1 by Robert Price at Tue Sep 24 00:12:48 EDT 2024

NAME

allocated for Robert Price

KEYWORD

allocated

STATUS

approved

A085793

Numbers k such that (k-1)*binomial(2k,k) + 1 is prime.
(history; published version)

#12 by Robert Price at Sun Sep 15 22:11:50 EDT 2024

STATUS

editing

proposed

#11 by Robert Price at Sun Sep 15 22:11:13 EDT 2024

DATA

2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 22, 23, 28, 31, 48, 49, 52, 80, 99, 167, 201, 295, 372, 381, 391, 638, 653, 720, 779, 887, 1047, 1454, 1647, 1719, 2405, 3234, 3257, 3542, 3623, 3765, 3796, 4337, 4490, 5228, 6507, 8544, 9990, 10000, 12478, 13479, 15487, 17115, 19856, 22753, 22995, 23114, 28895, 37120, 39855, 43027, 55908, 63350, 69845, 74001, 83600, 86095, 89897, 90761

COMMENTS

a(6869) > 10^5 - Robert Price, Sep 15 2024

LINKS

Robert Price, <a href="/A085793/b085793_1.txt">Table of n, a(n) for n = 1..68</a>

EXTENSIONS

a(53)-a(6768) from Robert Price, Sep 15 2024

#8 by Robert Price at Sun Sep 15 13:59:59 EDT 2024

STATUS

editing

proposed

#7 by Robert Price at Sun Sep 15 13:59:42 EDT 2024

DATA

COMMENTS

a(68) > 10^5 - Robert Price, Sep 15 2024

EXTENSIONS

a(53)-a(67) from Robert Price, Sep 15 2024

STATUS

approved

editing

A125240

Numbers k such that binomial(4k, k) - 1 is prime.
(history; published version)

#10 by Robert Price at Sun Sep 15 13:45:34 EDT 2024

STATUS

editing

proposed

#9 by Robert Price at Sun Sep 15 13:45:08 EDT 2024

DATA

1, 16, 36, 67, 95, 369, 383, 745, 1599, 2006, 2104, 2879, 3061, 9048, 9902, 12369, 15058, 18858, 21287, 22759, 24674, 33899, 43730, 55078, 86085

COMMENTS

a(26) > 10^5 - Robert Price, Sep 15 2024

EXTENSIONS

a(24)-a(25) from Robert Price, Sep 15 2024

STATUS

approved

editing

A125221

Numbers k such that binomial(3k, k) + 1 is prime.
(history; published version)

#16 by Robert Price at Tue Aug 13 13:53:54 EDT 2024

STATUS

editing

proposed