OFFSET
1,2
COMMENTS
a(n) purportedly gives the least k with A023193(k) = n; that is, this sequence should be the "least inverse" of A023193.
My web page extends the sequence to rho(305)=2047 and also gives a super-dense occurrence at rho(592)=4333 when pi(4333)=591 - the first known occurrence. - Thomas J Engelsma (tom(AT)opertech.com), Feb 16 2004
Tomás Oliveira e Silva (see link) has a table extending to n = 1000.
The minimal y such that there are n elements of {1, ..., y} with fewer than p distinct elements mod p for all prime p. - Charles R Greathouse IV, Jun 13 2013
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, (2nd edition, Springer, 1994), Section A9.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..672 (from Engelsma's data)
Thomas J. Engelsma, Permissible Patterns.
T. Forbes, Prime k-tuplets
Daniel M. Gordon and Gene Rodemich, Dense admissible sets, Proceedings of ANTS III, LNCS 1423 (1998), pp. 216-225.
D. Hensley and I. Richards, Primes in intervals, Acta Arith. 25 (1974), pp. 375-391.
H. L. Montgomery and R. C. Vaughan, The large sieve, Mathematika 20 (1973), pp. 119-134.
Tomás Oliveira e Silva, Admissible prime constellations
Ian Richards, On the incompatibility of two conjectures concerning primes; a discussion of the use of computers in attacking a theoretical problem, Bulletin of the American Mathematical Society 80:3 (1974), pp. 419-438.
H. Smith, On a generalization of the prime pair problem, Math. Comp., 11 (1957) 249-254.
Eric Weisstein's World of Mathematics, k-Tuple Conjecture.
FORMULA
Prime(floor((n+1)/2)) <= a(n) < prime(n) for large n. See Hensley & Richards and Montgomery & Vaughan. - Charles R Greathouse IV, Jun 18 2013
CROSSREFS
KEYWORD
nonn,nice
EXTENSIONS
Corrected and extended by David W. Wilson
STATUS
approved