login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A308416 Values of m for which 2*p + m cannot be a square when p is a prime. 0
1, 4, 8, 9, 13, 16, 17, 20, 24, 25, 28, 29, 33, 36, 37, 40, 41, 44, 48, 49, 52, 53, 56, 57, 61, 64, 65, 68, 69, 72, 73, 76, 80, 81, 84, 85, 88, 89, 92, 93, 97, 100, 101, 104, 105, 108, 109, 112, 113, 116, 120, 121, 124, 125, 128, 129, 132, 133, 136, 137, 141, 144, 145, 148, 149 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

m = i^2 + 4*j is a term for i > 0, 0 <= j < i. Proof: If p = 2, then i^2 < 2*p + m < (i+2)^2. Therefore (i+1)^2 = 4 + i^2 + 4*j, which leads to a contradiction. If p > 2 is such that 2*p + i^2 + 4*j = k^2, then k + i and k - i are both even numbers. Therefore 4 | 2*p + 4*j, which is also a contradiction.

The terms of this sequence can be obtained by starting with A042948 (numbers congruent to 0 or 1 mod 4) and deleting the terms of A028347 (n^2 - 4).

LINKS

Table of n, a(n) for n=1..65.

FORMULA

Conjecture: for k > 0 and 1 <= j <= k, a(2k^2-2j+1) = 4k^2+4k-4j-3, a(2k^2-2j+2) = 4k^2+4k-4j, a(2k^2+2k-2j+1) = 4k^2+8k-4j, a(2k^2+2k-2j+2) = 4k^2+8k-4j+1. - Jinyuan Wang, Jul 23 2019

PROG

(Python)

a=[]

a.append(0) #Offset starts at 1

iMax=15 #Example value

for i in range(1, iMax+1):

  for j in range(0, i):

   m=i*i+j*4

   a.append(m)

a.sort()

CROSSREFS

Cf. A042948, A028347.

Sequence in context: A235054 A292364 A071835 * A010429 A140282 A161757

Adjacent sequences:  A308413 A308414 A308415 * A308417 A308418 A308419

KEYWORD

nonn

AUTHOR

Bob Andriesse, May 25 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 03:22 EST 2020. Contains 338865 sequences. (Running on oeis4.)