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

1,1

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).

Links

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

Example

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.

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 *)

Prog

(PARI) {forprime(p=2, 250000, q=nextprime(p+1); m=0; j=p+1; while(j<q&&m<=7, f=factor(j); a=f[matsize(f)[1], 1]; if(m<a, m=a); j++); if(m==7, print1(p, ", ")))}

Crossrefs

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

Sequence in context: A028468 A146995 A102130 * A287307 A332255 A201121

Adjacent sequences: A080183 A080184 A080185 * A080187 A080188 A080189

Keyword

nonn

Author

Klaus Brockhaus, Feb 10 2003

Status

approved