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A344481 Isolated single primes enclosed by four composites on square spiral board of odd numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..51.

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

EXAMPLE

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).

PROG

(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<z2 else 8*n-5 if m<=z3 else -1 if m<=z4 else -8*n+9

    L[1]+=-1 if m==z1 else -8*n+15 if m<z2 else 1 if m<z3 else 8*n-3 if m<=z4 else -1

    L[2]+=8*n-9 if m==z1 else -1 if m<=z2 else -8*n+13 if m<z3 else i if m<z4 else 8*n-1

    L[3]+=8*n-7 if m<=z2 else -1 if m<=z3 else -8*n+11 if m<z4 else 1

    return L

for i in range(2, 200):

    p = prime(i); L1 = [2*neib(int((p+1)/2))[j]-1 for j in range(4)]

    if sum(isprime(k) for k in L1) == 0: print(p)

CROSSREFS

Cf. A341542.

Sequence in context: A000923 A142528 A139500 * A261376 A142094 A142212

Adjacent sequences:  A344478 A344479 A344480 * A344482 A344483 A344484

KEYWORD

nonn

AUTHOR

Ya-Ping Lu, May 20 2021

STATUS

approved

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Last modified September 24 22:33 EDT 2021. Contains 347651 sequences. (Running on oeis4.)