The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A345293 a(n) is the first number on the n-th layer in a layered square spiral of primes. 0
 2, 73, 149, 211, 307, 467, 659, 839, 1061, 1319, 1511, 1697, 1949, 2129, 2381, 2677, 2819, 3137, 3307, 3407, 3559, 3907, 4079, 4253, 4591, 4877, 5087, 5443, 5531, 5683, 5923, 6221, 6659, 6791, 6997, 7393, 7603, 8111, 8297, 8641, 8887, 9029, 9377, 9461, 9749 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first prime, 2, is placed at the origin with Cartesian coordinates of (0, 0, 0) and the second prime, 3, is placed at (1, 0, 0). The m-th prime (m >= 3) is placed by moving one unit forward in the direction from the (m-2)-th prime to the (m-1)-th prime, if the next prime is not a twin prime of the current one; otherwise, by turning 90 degrees counterclockwise and moving one unit forward. When it comes to a spot already occupied by another number, the prime is moved up one layer above the number. LINKS EXAMPLE First layer starts from 2 and second layer from 73.   59<--53<--47<--43<--41    |                   |   61   11<---7<---5   37     137<-131<-127<-113<-109<-107    |    |         |    |      |                        |   67   13    2--->3   31     139                      103    |    |              |                               |   71   17-->19-->23-->29      73-->79-->83-->89-->97->101 PROG (Python) from sympy import prime, nextprime print(2); d1 = 0; L = [0, 0, 0]; L1 = [] for i in range(1, 1501):     p = prime(i); np = nextprime(p); d = (d1 + 1)%4 if np - p == 2 else d1     L[0] += 1 if d == 0 else -1 if d == 2 else 0     L[1] += 1 if d == 1 else -1 if d == 3 else 0     if L in L1: L[2] += 1; print(np)     L1.append([L[0], L[1], L[2]]); d1 = d CROSSREFS Cf. A063826, A136626. Sequence in context: A276518 A297410 A041647 * A083018 A240174 A295172 Adjacent sequences:  A345290 A345291 A345292 * A345294 A345295 A345296 KEYWORD nonn AUTHOR Ya-Ping Lu, Jun 13 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)