OFFSET
2,2
COMMENTS
Sequence lists the maxima of rows of triangle A207409. - Michel Marcus, Oct 01 2013
If there is a prime q with p/2 < q < 2p/3, then p mod q = p - q and a(n) = p - nextprime(p/2). But by a result of Nagura, there is always a prime between x and 6x/5 for x > 25, so this holds for all p > 50 and (checking 2 <= n <= 15) for all n > 1. - Charles R Greathouse IV, Jul 12 2024
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 2..10000
Jitsuro Nagura, On the interval containing at least one prime number, Proc. Japan Acad. 28: 177-181, 1952.
FORMULA
a(n) = p - nextprime(p/2), where p is the n-th prime, see Greathouse comment. - Charles R Greathouse IV, Jul 12 2024
MAPLE
a := proc(n) ithprime(n); % - nextprime(iquo(%, 2)) end: seq(a(n), n = 2..63);
# Peter Luschny, Jul 13 2024 (after Charles R Greathouse IV)
MATHEMATICA
Map[# - NextPrime[#/2] &, Prime[Range[2, 100]]] (* Paolo Xausa, Jul 15 2024, after Charles R Greathouse IV *)
PROG
(PARI) a(n)=maxp = 0; for (i = 1, n-1, mp = prime(n) % prime(i); maxp = max(mp, maxp); ); maxp; \\ Michel Marcus, Oct 01 2013
(PARI) P=primes(100); vector(#P, i, mx=0; for(j=1, i-1, mx=max(P[i]%P[j], mx)); mx)[2..#P] \\ Charles R Greathouse IV, Oct 01 2013
(PARI) a(n) = my(p=prime(n)); p - nextprime(p/2) \\ Charles R Greathouse IV, Jul 12 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved