

A187677


Primes of the form 8n^2 + 6n  1 for positive n.


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

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*n1) \\ 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


AUTHOR

Alonso del Arte, Mar 21 2011


STATUS

approved



