

A080186


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


2



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
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OFFSET

1,1


COMMENTS

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



