A180641 Primes P such that P > (largest prime factor of (P-1)) * (largest prime factor of (P+1)).

7, 17, 19, 31, 41, 53, 71, 79, 89, 97, 101, 109, 127, 151, 163, 181, 191, 197, 199, 239, 241, 251, 257, 271, 307, 337, 349, 379, 401, 419, 431, 433, 449, 461, 463, 487, 491, 499, 521, 571, 577, 593, 599, 601, 631, 641, 647, 659, 683, 701, 727, 751, 769, 809

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

Example: For n = 3, a(3)=19.
The prime P = 19
P-1 = 18 (largest prime factor of 18 is 3)
P+1 = 20 (largest prime factor of 20 is 5)
19 > 3*5.

Mathematica

lpfQ[n_]:=Module[{a=FactorInteger[n-1][[-1, 1]], b=FactorInteger[n+1][[-1, 1]]}, n>a*b]; Select[Prime[Range[200]], lpfQ] (* Harvey P. Dale, Aug 16 2013 *)

Prog

(PARI) lpf(n) = {f = factor(n); return (f[#f~, 1]); }
lista(nn) = {forprime(p=3, nn, if ((p > lpf(p-1)*lpf(p+1)), print1(p, ", "); ); ); } \\ Michel Marcus, Jul 25 2013

Crossrefs

Cf. A180640. See also A103666, A103667.

Sequence in context: A106123 A156011 A155774 * A234095 A354168 A287182

Adjacent sequences: A180638 A180639 A180640 * A180642 A180643 A180644

Keyword

nonn

Author

Karl Hovekamp, Sep 14 2010

Status

approved