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

1,1

Links

Table of n, a(n) for n=1..43.

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A001359, A054554, A163633.

Sequence in context: A181291 A038703 A283806 * A074931 A023226 A113169

Adjacent sequences: A163583 A163584 A163585 * A163587 A163588 A163589

Keyword

nonn

Author

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

Extensions

Edited by Georg Fischer, Dec 03 2024

Status

approved