A163586 a(1) = 3. For n > 1, Ulam's spiral is started with a(n-1), and the primes p on the NE spoke are considered. a(n) is the minimal p that is the lesser of a twin prime pair.

3, 5, 17, 29, 41, 71, 101, 191, 281, 311, 617, 857, 1319, 1451, 1481, 1721, 2027, 2267, 2729, 2969, 2999, 3461, 3767, 4229, 4241, 4271, 20021, 22091, 22961, 23201, 23291, 27581, 31121, 31151, 31181, 32441, 32531, 32561, 32801, 32831, 33071, 33827, 35897

Offset: 1

Author

Milton L. Brown (miltbrown(AT)earthlink.net), Jul 31 2009

Keywords

• nonn

Examples

			Spiral for a(2)=5:
 21 20 19 18 17
 22 .9 .8 .7 16
 23 10 .5 .6 15
 24 11 12 13 14
 25 26 27 28 29
a(2)+4*k^2-2*k with k=1 is not taken since 7 is no lesser twin prime, but 17 (k=2) is.
		

Crossrefs

Cf. A001359, A054554, A163633.

Programs

PARI

twinp(p) = if(isprime(p) && isprime(p + 2),1,0);
ulamNW(p, k) = p + 4*k^2-2*k;
p = 1; for(n=1, 64, k=1; while (!twinp(ulamNW(p,k)), k++); p = ulamNW(p, k); print1(", ", p)) \\ Georg Fischer, Dec 03 2024

Formula

The terms on the NE spoke are given by a(n - 1) + 4*k^2 - 2*k for k >= 1.

Extensions

Edited by Georg Fischer, Dec 03 2024