The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A130290

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A130290

Number of nonzero quadratic residues modulo the n-th prime.
(history; published version)

#49 by Sean A. Irvine at Sat Jan 21 15:08:33 EST 2023

STATUS

proposed

approved

#48 by Andrew Howroyd at Sun Jan 01 11:04:01 EST 2023

STATUS

editing

proposed

Discussion

Sun Jan 01

11:21

Michel Marcus: allo ?  are you there ??

#47 by Andrew Howroyd at Sun Jan 01 11:03:29 EST 2023

COMMENTS

a(n) is the number of pairs (a,b) such that a + b = prime(n) with 1 <= a <= b. - Nicholas Leonard, Oct 02 2022

Discussion

Sun Jan 01

11:04

Andrew Howroyd: Ok?

#46 by Andrew Howroyd at Sun Jan 01 11:02:10 EST 2023

COMMENTS

Conjecture: Also a(n)is the number of solutions to pairs (a,b) such that a + b = prime(n), where 0 with 1 < = a <= b and gcd(a, b) = 1. Holds for the first 1000 primes. - Nicholas Leonard, Oct 02 2022

STATUS

proposed

editing

#45 by Charles R Greathouse IV at Sun Dec 11 08:22:57 EST 2022

STATUS

editing

proposed

Discussion

Sun Jan 01

10:58

Andrew Howroyd: 1) Is gcd(a,b)=1 necessary? (If there were a common factor a + b would not be prime). 2) The conjecture seems trivially true given first formula: a(n) = floor( A000040(n)/2 ).

#44 by Charles R Greathouse IV at Sun Dec 11 08:18:10 EST 2022

COMMENTS

Conjecture: Also the number of solutions to a + b = prime(n), where and 0 < a <= b are positive integers and gcd(a, b) = 1 and either a < b or a = b. Holds for the first 1000 primes. - Nicholas Leonard, Oct 02 2022

CROSSREFS

Cf. A005097 (Odd primes - 1)/2, A102781 (Integer part of n#/(n-2)#/2#), A102781 (Number of even numbers less than the n-th prime), A063987 (quadratic residues modulo the n-th prime), A006254 (Numbers n such that 2n-1 is prime), A111333 (Number of odd numbers <= n-th prime), A000040 (prime numbers), A130291.

STATUS

proposed

editing

Discussion

Sun Dec 11

08:22

Charles R Greathouse IV: Since the numbers are positive and less than prime(n), they are necessarily relatively prime -- if they had a prime factor in common, it would have to be prime(n). So the conjecture is true.

#43 by Michel Marcus at Sun Dec 11 06:25:24 EST 2022

STATUS

editing

proposed

#42 by Michel Marcus at Sun Dec 11 06:25:15 EST 2022

COMMENTS

From _Conjecture: Also the number of solutions to a + b = prime(n), where and b are positive integers and gcd(a, b) = 1 and either a < b or a = b. Holds for the first 1000 primes. - _Nicholas Leonard_, Oct 2 02 2022: (Start)

Conjecture: Also the number of solutions to a + b = prime(n), where and b are positive integers and gcd(a, b) = 1 and either a < b or a = b. Holds for the first 1000 primes. (End)

STATUS

proposed

editing

Discussion

Sun Dec 11

06:25

Michel Marcus: signature fixed

#41 by Joerg Arndt at Thu Dec 08 05:25:28 EST 2022

STATUS

editing

proposed

Discussion

Sat Dec 10

08:07

Hugo Pfoertner: Regardless of whether the comment is accepted or not, there is no need for a block signature.

#40 by Nicholas Leonard at Sun Oct 02 17:56:26 EDT 2022

COMMENTS

Conjecture: Also the number of solutions to a + b = prime(n), where and b are positive integers and gcd(a, b) = 1 and either a < b or a = b. Holds for the first 1000 primes. (End)

Discussion

Mon Dec 05

14:37

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A130290 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

Thu Dec 08

05:25

Joerg Arndt: Not sure this should stay.