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 A341542 Numbers on the square spiral board that are enclosed by four primes. 6
 12, 72, 1152, 1452, 1950, 3672, 5520, 6660, 8232, 10302, 10890, 13218, 15288, 15360, 16062, 18042, 20898, 21018, 23628, 25998, 27918, 32190, 37812, 42018, 42462, 48858, 55818, 57192, 80832, 80910, 83340, 91368, 97848, 98640, 104472, 111492, 117498, 119550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is similar to A172294, in which the starting number of the square spiral is 0 instead of 1. For a(n) < 10000000, 4 out of the 782 terms in this sequence, 72, 10302, 415380 and 1624350 are absent in A172294, while 6 out of the 784 terms in A172294, 42, 23562, 83232, 205662, 5805690 and 7019850 are absent in this sequence. Conjecture: This sequence is infinite. If the conjecture holds, then the twin prime conjecture is true. The 4 neighbors of n in the spiral are A068225, A068226, A334751, and A334752. - Kevin Ryde, Feb 13 2021 LINKS Table of n, a(n) for n=1..38. PROG (Python) from sympy import isprime from math import sqrt, ceil m, m_max = 2, 1000000 while m <= m_max: L = [0, 0, 0, 0] n = int(ceil((sqrt(m) + 1.0)/2.0)) 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 if m > z1 and m < z2: L = [m + 1, m - 8*n + 15, m - 1, m + 8*n - 7] elif m > z2 and m < z3: L = [m + 8*n - 5, m + 1, m - 8*n + 13, m - 1] elif m > z3 and m < z4: L = [m - 1, m + 8*n - 3, m + 1, m - 8*n + 11] elif m > z4 and m < z5: L = [m - 8*n + 9, m - 1, m + 8*n - 1, m + 1] if isprime(L[0]) == 1 and isprime(L[1]) == 1 and isprime(L[2]) == 1 and isprime(L[3]) == 1: print(m) m += 2 CROSSREFS Cf. A341541, A341672, A172294, A068225, A068226, A334751, and A334752. Sequence in context: A320660 A108734 A143559 * A120793 A120783 A103475 Adjacent sequences: A341539 A341540 A341541 * A341543 A341544 A341545 KEYWORD nonn AUTHOR Ya-Ping Lu, Feb 13 2021 STATUS approved

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Last modified October 3 16:08 EDT 2023. Contains 365868 sequences. (Running on oeis4.)