login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I #12 Jan 04 2020 09:51:49

%S 13,41,419,881,1049,2267,2687,3359,3527,5879,6299,7349,7559,8231,8819,

%T 10499,18521,26249,26879,28349,29399,30869,33599,35279,49391,81647,

%U 100799,102059,131249,131711,134399,158759,170099,183707,197567,241919

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

%C 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).

%H Amiram Eldar, <a href="/A080186/b080186.txt">Table of n, a(n) for n = 1..200</a> (terms 1..100 from Harvey P. Dale)

%e 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.

%t 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 *)

%o (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,",")))}

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

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Feb 10 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)