A344481 Isolated single primes enclosed by four composites on square spiral board of odd numbers.

97, 157, 233, 257, 293, 307, 331, 337, 359, 367, 389, 397, 409, 439, 449, 479, 487, 499, 503, 563, 607, 613, 631, 653, 677, 683, 691, 709, 727, 743, 751, 761, 773, 853, 863, 887, 907, 911, 929, 937, 967, 971, 983, 1013, 1069, 1087, 1117, 1181, 1187, 1193, 1201

Offset: 1

Author

Ya-Ping Lu, May 20 2021

Keywords

• nonn

Examples

			3 is not a term because two of the four neighbors (1, 5, 17 and 21) are primes.
97 is a term because 97 is a prime and all four neighbors (51, 95, 99 and 159) are composites (see the illustration in Links).
		

Links

• Ya-Ping Lu, Illustration of isolated single primes on square spiral board

Crossrefs

Cf. A341542.

Programs

Python

from sympy import prime, isprime; from math import sqrt, ceil
def neib(m):
    n = int(ceil((sqrt(m)+1.0)/2.0)); L = [m,m,m,m]
    z1=4*n*n-12*n+10;z2=4*n*n-10*n+7;z3=4*n*n-8*n+5;z4=4*n*n-6*n+3;z5=4*n*n-4*n+1
    L[0]+=1 if m