

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
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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

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 betterknown 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


CROSSREFS

Cf. A073337 and A168026 are diagonals of the usual Ulam spiral which have some of the same primes as this vertical line.


KEYWORD

easy,nonn


AUTHOR



STATUS

approved



