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A283791
Prime numbers p such that all prime factors of p+1 and p-1 are smaller than the cube root of p.
1
449, 4159, 4801, 4999, 8191, 11551, 11969, 15731, 16561, 22541, 26449, 28729, 31249, 33857, 35153, 38501, 39929, 42283, 45631, 46817, 47431, 47501, 48049, 51679, 52021, 62929, 63799, 68449, 69191, 81919, 83231, 84967, 89909, 94771, 97499, 100049, 104059
OFFSET
1,1
EXAMPLE
449 is a prime number. 449+1 = 450 = 2*3^2*5^2, 5^3 = 125 < 449; 449-1 = 448 = 2^6*7, 7^3 = 343 < 449, so 449 is in this list.
457 is a prime number. 457+1 = 458 = 2*229, 229^3 > 457, so 457 is NOT in this list.
MATHEMATICA
p = 1; Table[
While[p = NextPrime[p]; fp = Last[FactorInteger[p + 1]][[1]];
fm = Last[FactorInteger[p - 1]][[1]]; (fp^3 >= p) || (fm^3 >=
p)]; p, {n, 1, 37}]
PROG
(PARI) isok(p) = isprime(p) && (p>2) && (vecmax(factor(p-1)[, 1])^3 < p) && (vecmax(factor(p+1)[, 1])^3 < p); \\ Michel Marcus, Jan 10 2018
CROSSREFS
Cf. A000040.
Sequence in context: A135073 A160291 A193255 * A036945 A201182 A012169
KEYWORD
nonn,easy
AUTHOR
Lei Zhou, Mar 16 2017
EXTENSIONS
Definition corrected by Zak Seidov, Dec 04 2017
STATUS
approved