A080186 Primes p such that 7 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248).

13, 41, 419, 881, 1049, 2267, 2687, 3359, 3527, 5879, 6299, 7349, 7559, 8231, 8819, 10499, 18521, 26249, 26879, 28349, 29399, 30869, 33599, 35279, 49391, 81647, 100799, 102059, 131249, 131711, 134399, 158759, 170099, 183707, 197567, 241919

Offset: 1

Author

Klaus Brockhaus, Feb 10 2003

Keywords

• nonn

Comments

The sequence appears to consist of 13 and the lesser of twin primes q (A001359) such that q+1 is 7-smooth (A002473) but not 5-smooth (A051037, A080194).

Examples

			13 is a term since 14 = 2*7, 15 = 3*5, 16 = 2^4 are the numbers between 13 and the next prime 17; 419 is a term since 420 = 2^2*3*5*7 is the only number between 419 and the next prime 421.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..200 (terms 1..100 from Harvey P. Dale)

Crossrefs

Cf. A052248, A001359, A002473, A051037, A080194.

Programs

Mathematica

lpf7Q[n_]:=Max[Flatten[Transpose[FactorInteger[#]][[1]]&/@Range[ n+1, NextPrime[ n]-1]]]==7; Select[Prime[Range[22000]],lpf7Q] (* Harvey P. Dale, Sep 25 2015 *)

PARI

{forprime(p=2,250000,q=nextprime(p+1); m=0; j=p+1; while(j