A117098 Numbers n such that nextprime(5*n)<5*nextprime(n) (if p is prime then nextprime(p)=p).

1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 20, 21, 22, 24, 25, 26, 27, 30, 32, 33, 34, 35, 36, 38, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 64, 65, 66, 68, 69, 70, 74, 75, 76, 77, 80, 81, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 98, 99, 100

Offset

1,2

Comments

denote f(x)=nextprime(x) let A(p)={n/f(p*n)<f(p)*f(n)} and A(q)={n/f(q*n)<f(q)*f(n)} (q,p are prime) if q<p all terms of A(q) are in A(p). if B(p)={n/f(p*n)>f(p)*f(n)} I conjectured that when p --> infinity, A(p) = All composite positive integers when p --> infinity, B(p) = All primes numbers

Links

Harvey P. Dale, Table of n, a(n) for n = 1..2000

Example

nextprime(5*4)=23 and nextprime(5)*nextprime(4)=5*5=25 then 4 is member because 23<15

Mathematica

np5Q[n_]:=Module[{np=If[PrimeQ[n], n, NextPrime[n]]}, NextPrime[5n]<5np]; Select[ Range[100], np5Q] (* Harvey P. Dale, Jun 12 2022 *)

Prog

(PARI) for(i=1, 100, if(nextprime(5*i)<nextprime(5)*nextprime(i), print1(i, ", ")))

Crossrefs

Sequence in context: A329149 A202259 A050655 * A077136 A098216 A341321

Adjacent sequences: A117095 A117096 A117097 * A117099 A117100 A117101

Keyword

easy,nonn

Author

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 18 2006

Status

approved