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A172979
Primes with locations of right angle turns in Ulam square spiral (primes in A033638).
3
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 21 2010
STATUS
approved