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A078784 Primes on axis of Ulam square spiral (with rows ... / 7 8 9 / 6 1 2 / 5 4 3 / ... ) with origin at (1). 1
2, 11, 19, 23, 53, 61, 127, 139, 151, 163, 233, 281, 431, 541, 613, 743, 827, 977, 1009, 1279, 1621, 1871, 2003, 2281, 2377, 2731, 3109, 3221, 3511, 3571, 3631, 3691, 4001, 4129, 4523, 4591, 5077, 6361, 6521, 7789, 7877, 8419, 9851, 10151, 10973, 11503, 11719, 11827, 12377, 12601, 12713, 13399 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Quadrants are numbered clockwise - 4=north, 1=east, 2=south, 3=west. The spiral numbers falling on axes (whether prime or not) are 4=north (2n+1)^2-n, 1=east (2n+1)^2+n+1, 2=south (2n)^2-(n-1), 3=west (2n)^2+n+1.

Primes to the left, right, above or below the 1 in the example in A054552.

This is the union of the primes in A168022, A168023, A168025 and A168027. - R. J. Mathar, Jul 11 2014

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

For example, n=0, quadrant = 1, a(1)=2, distance = 1 ex. n = 1, quadrant=1, a(2)=11, distance =2 ex. n=2, q=3, a(3)=19, distance = 2, ...

MATHEMATICA

Select[ Sort@ Flatten@ Table[ 4n^2 + (2j - 3)n + 1, {j, 0, 3}, {n, 58}], PrimeQ] (* Robert G. Wilson v, Jul 10 2014 *)

CROSSREFS

Cf. A054552, A054556, A054567, A033951, A172979.

Sequence in context: A079062 A038930 A019375 * A117196 A304811 A064739

Adjacent sequences:  A078781 A078782 A078783 * A078785 A078786 A078787

KEYWORD

nonn

AUTHOR

Donald S. McDonald, Jan 10 2003

EXTENSIONS

a(12) onward from Robert G. Wilson v, Jul 10 2014

STATUS

approved

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Last modified February 17 02:33 EST 2019. Contains 320200 sequences. (Running on oeis4.)