A172979 Primes with locations of right angle turns in Ulam square spiral (primes in A033638).

2, 3, 5, 7, 13, 17, 31, 37, 43, 73, 101, 157, 197, 211, 241, 257, 307, 401, 421, 463, 577, 601, 677, 757, 1123, 1297, 1483, 1601, 1723, 2551, 2917, 2971, 3137, 3307, 3541, 3907, 4357, 4423, 4831, 5113, 5477, 5701, 6007, 6163, 6481, 7057, 8011, 8101, 8191, 8837, 9901

Offset

1,1

Comments

Except for the first term, 2, these are the primes on the main diagonals of the Ulam spiral. - Robert G. Wilson v, Jul 10 2014

Links

Table of n, a(n) for n=1..51.

Example

Ulam square spiral = 7 8 9 / 6 1 2 / 5 4 3 /...; changes of direction (right-angle)
  for the primes at 2 3 5 7 ...

Maple

with(numtheory): a0:=1:for n from 1 to 200 do : a1:=a0+floor(n/2):a0:=a1:if
  type(a1, prime)=true then printf(`%d, `, a1):else fi:od:

Mathematica

Select[ Sort@ Flatten@ Table[ 4n^2 + (2j - 4)n + 1, {j, 0, 3}, {n, 55}], PrimeQ]

Prog

(PARI) for(n=0, 10^3, my(t=n^2\4+1); if(isprime(t), print1(t, ", "))); \\ Joerg Arndt, Jul 12 2014

Crossrefs

Cf. A033638, A054554, A053755, A054569, A016754, A078784.

Sequence in context: A087520 A117159 A134873 * A118724 A055387 A046732

Adjacent sequences: A172976 A172977 A172978 * A172980 A172981 A172982

Keyword

nonn

Author

Michel Lagneau, Nov 21 2010

Status

approved