login
This site is supported by donations 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.

LINKS

Table of n, a(n) for n=1..36.

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.

Sequence in context: A132233 A282322 A031382 * A082040 A106734 A066465

Adjacent sequences:  A187674 A187675 A187676 * A187678 A187679 A187680

KEYWORD

easy,nonn,changed

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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 20 08:50 EDT 2018. Contains 313914 sequences. (Running on oeis4.)