login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187677 Primes of the form 8k^2 + 6k - 1 for positive k. 1
13, 43, 89, 151, 229, 433, 701, 859, 1033, 1223, 1429, 1889, 2143, 2699, 3001, 3319, 4003, 4751, 5563, 7873, 10009, 11173, 11779, 12401, 13693, 17203, 18719, 19501, 21943, 25423, 27259, 28201, 30133, 31123, 33151, 36313 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
In a variant of the Ulam spiral in which only odd numbers are entered, some primes still line up along some diagonals but not others. Without the even numbers, primes can also line up in horizontal and diagonal lines. This sequence comes from an upwards vertical line which starts with 13.
Primes of A091823. - Klaus Purath, Jan 03 2021
LINKS
OEIS Wiki, Ulam spiral
Alonso del Arte, Ulam spiral (2009). [EmdrGreg's comment suggested the odd number spiral variant.]
FORMULA
a(n) = 2((2n - 1)^2 - n) - 1 (or, find the number in the corresponding spot in the better-known Ulam spiral, double it and subtract 1).
The polynomial 8n^2 - 10n + 1 produces the same primes.
MATHEMATICA
Select[Table[2((2n - 1)^2 - n) - 1, {n, 100}], PrimeQ]
PROG
(Magma) [ a: n in [0..2500] | IsPrime(a) where a is 8*n^2 + 6*n - 1 ]; // Vincenzo Librandi, apr 24 2011
(PARI) is(n)=n>9 && isprime(8*n^2+6*n-1) \\ Charles R Greathouse IV, Jan 21 2016
CROSSREFS
Cf. A073337 and A168026 are diagonals of the usual Ulam spiral which have some of the same primes as this vertical line.
Cf. A091823.
Sequence in context: A132233 A282322 A031382 * A082040 A106734 A066465
KEYWORD
easy,nonn
AUTHOR
Alonso del Arte, Mar 21 2011
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 18 04:54 EDT 2024. Contains 374377 sequences. (Running on oeis4.)