OFFSET
3,1
COMMENTS
The same selection rule as in A078497 applies: if there is more than one prime triple (p,q=p+d,r=q+d) with p+q+r=A001748(n), take p from the triple with minimum d. - R. J. Mathar, May 19 2007
a(n) is the greatest prime p less than prime(n) such that 2*prime(n) - p is also prime. - Andrew Howroyd, Jul 30 2026
LINKS
Andrew Howroyd, Table of n, a(n) for n = 3..10000
FORMULA
A078497(n)-prime(n)=prime(n)-a(n)=d. - R. J. Mathar, May 19 2007
Conjecture: Limit_{N->oo} (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n+2)) = 1. - Alain Rocchelli, May 01 2024
a(n) = prime(n) - A078611(n). - Andrew Howroyd, Jul 30 2026
EXAMPLE
3 + 5 + 7 = 15, which is three times the 3rd prime number. Thus a(3) = 3.
MAPLE
A129758 := proc(n) local p3, i, d, r, p; p3 := ithprime(n) ; i := n+1 ; while true do r := ithprime(i) ; d := r-p3 ; p := p3-d ; if isprime(p) then RETURN(p) ; fi ; i := i+1 ; od ; RETURN(-1) ; end: for n from 3 to 60 do printf("%d, ", A129758(n)) ; od ; # R. J. Mathar, May 19 2007
MATHEMATICA
a[n_]:=Module[{}, k=1; While[Not[PrimeQ[Prime[n+1]-k] && PrimeQ[Prime[n+1]+k]], k++ ]; Prime[n + 1] - k]; Table[a[n], {n, 2, 60}]
PROG
(PARI) a(n) = {my(p=prime(n)); forstep(d=2, p, 2, if(isprime(p-d)&&isprime(p+d), return(p-d))); oo} \\ Andrew Howroyd, Jul 30 2026
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, May 15 2007
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 30 2026
STATUS
approved