A117093 Numbers k such that nextprime(3*k) > 3*nextprime(k) (if p is prime then nextprime(p) = p).
2, 3, 5, 7, 11, 13, 16, 17, 18, 19, 23, 28, 29, 30, 31, 37, 38, 39, 40, 41, 43, 47, 53, 58, 59, 61, 67, 71, 72, 73, 78, 79, 81, 82, 83, 88, 89, 95, 96, 97, 98, 99, 100, 101, 103, 106, 107, 108, 109, 113, 127, 130, 131, 137, 138, 139, 148, 149, 150, 151, 156, 157
Offset: 1
Examples
13 is a term since nextprime(3*13) = 41 and 3*nextprime(13) = 3*13=39 and 41 > 39.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
filter:= n -> nextprime(3*n) > 3*nextprime(n-1): select(filter, [$1..1000]); # Robert Israel, Jul 25 2025
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Mathematica
fp[k_]:=If[PrimeQ[k],k,NextPrime[k]];Select[Range[160],fp[3#]>3fp[#]&] (* James C. McMahon, Aug 23 2024 *)
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PARI
for(i=1,100,if(nextprime(3*i)>nextprime(3)*nextprime(i),print1(i,", ")))
Extensions
a(44)-a(59) from James C. McMahon, Aug 23 2024
Comments