A080188 Primes p such that 13 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248).

23, 311, 349, 857, 1091, 1871, 1949, 2027, 2339, 2729, 3119, 3821, 5849, 6551, 7487, 9437, 10139, 10529, 11699, 15287, 18251, 21059, 21839, 38609, 42899, 49919, 51479, 57329, 61151, 65519, 69497, 70199, 70979, 81899, 97499, 108107, 109199, 114659

Offset

1,1

Comments

The sequence appears to consist of 23, 349 and the lesser of twin primes q (A001359) such that q+1 is 13-smooth (A080197) but not 11-smooth (A051038, A080196).

Links

Amiram Eldar, Table of n, a(n) for n = 1..1092 (terms below 10^11)

Example

349 is a term since 350 = 2*5^2*7, 351 = 3^3*13, 352 = 2^5*11 are the numbers between 349 and the next prime 353; 857 is a term since 858 = 2*3*11*13 is the only number between 857 and the next prime 859.

Mathematica

maxPrime[n1_, n2_] := FactorInteger[#][[-1, 1]] & /@ Range[n1, n2]; Select[Range[120000], PrimeQ[#] && Max[maxPrime[# + 1, NextPrime[#] - 1]] == 13 &] (* Amiram Eldar, Feb 08 2020 *)

Prog

(PARI) {forprime(p=2, 120000, q=nextprime(p+1); m=0; j=p+1; while(j<q&&m<=13, f=factor(j); a=f[matsize(f)[1], 1]; if(m<a, m=a); j++); if(m==13, print1(p, ", ")))}

Crossrefs

Cf. A052248, A001359, A080197, A051038, A080196.

Sequence in context: A086558 A090927 A045530 * A142433 A234234 A125458

Adjacent sequences: A080185 A080186 A080187 * A080189 A080190 A080191

Keyword

nonn

Author

Klaus Brockhaus, Feb 10 2003

Status

approved