A078784 Primes on axis of Ulam square spiral (with rows ... / 7 8 9 / 6 1 2 / 5 4 3 / ... ) with origin at (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

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 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