

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
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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)^2n, 1=east (2n+1)^2+n+1, 2=south (2n)^2(n1), 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 n=0, quadrant = 1, a(1) = 2, distance = 1;
for n=1, quadrant = 1, a(2) = 11, distance = 2;
for n=2, quadrant = 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



