A283791 Prime numbers p such that all prime factors of p+1 and p-1 are smaller than the cube root of p.

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

Links

Lei Zhou, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A283788 A283789 A283790 * A283792 A283793 A283794

Keyword

nonn,easy

Author

Lei Zhou, Mar 16 2017

Extensions

Definition corrected by Zak Seidov, Dec 04 2017

Status

approved