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%I #30 Sep 08 2022 08:45:56
%S 13,43,89,151,229,433,701,859,1033,1223,1429,1889,2143,2699,3001,3319,
%T 4003,4751,5563,7873,10009,11173,11779,12401,13693,17203,18719,19501,
%U 21943,25423,27259,28201,30133,31123,33151,36313
%N Primes of the form 8k^2 + 6k - 1 for positive k.
%C 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.
%C Primes of A091823. - _Klaus Purath_, Jan 03 2021
%H OEIS Wiki, <a href="/wiki/Ulam_spiral#Odd numbers Ulam spiral">Ulam spiral</a>
%H Alonso del Arte, <a href="http://www.youtube.com/watch?v=dx24qqBc-PY">Ulam spiral</a> (2009). [EmdrGreg's comment suggested the odd number spiral variant.]
%F 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).
%F The polynomial 8n^2 - 10n + 1 produces the same primes.
%t Select[Table[2((2n - 1)^2 - n) - 1, {n, 100}], PrimeQ]
%o (Magma) [ a: n in [0..2500] | IsPrime(a) where a is 8*n^2 + 6*n - 1 ]; // _Vincenzo Librandi_, apr 24 2011
%o (PARI) is(n)=n>9 && isprime(8*n^2+6*n-1) \\ _Charles R Greathouse IV_, Jan 21 2016
%Y Cf. A073337 and A168026 are diagonals of the usual Ulam spiral which have some of the same primes as this vertical line.
%Y Cf. A091823.
%K easy,nonn
%O 1,1
%A _Alonso del Arte_, Mar 21 2011