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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 (list; graph; refs; listen; history; text; internal format)
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

Harvey P. Dale, Table of n, a(n) for n = 1..100

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 A201121 A116153

Adjacent sequences:  A080183 A080184 A080185 * A080187 A080188 A080189

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Feb 10 2003

STATUS

approved

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Last modified August 25 16:17 EDT 2019. Contains 326324 sequences. (Running on oeis4.)