A059428 Number of points of rotation in a prime block spiral.

2, 3, 5, 11, 17, 29, 41, 59, 73, 101, 127, 157, 191, 229, 269, 313, 367, 421, 467, 547, 607, 673, 751, 829, 919, 1013, 1093, 1201, 1297, 1429, 1523, 1621, 1753, 1889, 2027, 2153, 2309, 2441, 2621, 2749, 2909, 3089, 3299, 3463, 3623, 3821, 4007, 4217, 4421

Offset

1,1

Comments

Analogous to A002620 except primes are substituted for the natural numbers.

Links

Table of n, a(n) for n=1..49.

Formula

Arrange primes in a block spiral formation. a(n) is determined by the point of rotation to allow for continuation of the sequence.

a(n) = prime(A002620(n)+1). - Ya-Ping Lu, Sep 18 2025

Example

Spiral begins:
   (73)-79--83--89--97-(101)
     |                    |
    71 (17)-19--23-(29)  etc.
     |   |           |
    67  13  (2)-(3) 31
     |   |       |   |
    61 (11)--7--(5) 37
     |               |
   (59)-53--47--43-(41)

Maple

A059428 := proc(n) RETURN(ithprime(1+floor(n^2/4))) end: # Francisco Salinas (franciscodesalinas(AT)hotmail.com), Jan 05 2002

Prog

(Python)
from sympy import prime
def A059428(n): return prime(((n*n)>>2)+1) # Ya-Ping Lu, Sep 18 2025

Crossrefs

Sequence in context: A063091 A394509 A124588 * A084571 A345471 A073021

Adjacent sequences: A059425 A059426 A059427 * A059429 A059430 A059431

Keyword

easy,nonn

Author

Jason Earls, Mar 15 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 19 2001

Status

approved