A072664 -id:A072664 - cp's OEIS frontend

A093552 a(n) is the smallest number m such that m-k is product of k+1 primes for k=0,1,2,...,n.

2, 5, 47, 107, 71999, 392279, 305778479, 24405534719, 899133243623

Offset: 0

Farideh Firoozbakht, Apr 14 2004

Each term of this sequence is prime.

			a(5)=392279 because:
392279 is prime;
392279-1 = 2*196139;
392279-2 = 3*229*571;
392279-3 = 2*2*281*349;
392279-4 = 5*5*13*17*71;
392279-5 = 2*3*3*19*31*37;
392279 is the smallest number m such that m-k is product of k+1 primes for k=0,1,2,3,4 & 5.

Cf. A072664, A072875, A086560.

Table[m = 1; While[Table[Plus @@ Last /@ FactorInteger[Prime[m] - k], {k, 0, n}] != Range[1, n + 1], m++]; Prime[m], {n, 0, 5}] (* Robert Price, Jun 09 2019 *)

a(6) corrected by Mike Oakes, Jun 20 2012
a(7) from Zak Seidov, Apr 23 2017
a(8) from Giovanni Resta, Apr 27 2017

A072665 Center of smallest run of 2n+1 consecutive numbers with exactly n+1,n,...,2,1,2,...,n,n+1 distinct prime factors, respectively.

Original entry on oeis.org

2, 11, 2917

Offset: 0

Rick L. Shepherd, Jul 30 2002

Borrowing from musical terminology, these could be considered "swells" of primality - first a crescendo ("more prime"), then a decrescendo ("less prime"). a(3), if it exists, is greater than 70750000. The corresponding sequence but counting prime factors with multiplicity (A001222) has only two terms (2, 5) because either the number immediately before or after any odd center > 5 equals 4k for some k >= 2, and thus has at least three prime factors, not exactly two, when duplicates are counted.

a(3) > 10^63. - Hiroaki Yamanouchi, Sep 25 2014

			a(0) = 2 (prime) is the smallest number with one prime factor. a(1) = 11 as 10 (=2*5), 11 (prime) and 12 (=2^2*3) have 2,1,2 distinct prime factors (A001221), respectively and there is no smaller center of such a run. a(2) = 2917 as 2915 (=5*11*53), 2916 (=2^2*3^6), 2917 (prime), 2918 (=2*1459) and 2919 (=3*7*139) have 3,2,1,2,3 distinct prime factors and there is no smaller such run.

Cf. A072664 (smallest finish with run pattern n, ..., 2, 1), A086560 (smallest start with run pattern 1, 2, ..., n), A001221 (omega).

Comment expanded and small typos fixed by Rick L. Shepherd, Jun 22 2017

cp's OEIS Frontend

A093552 a(n) is the smallest number m such that m-k is product of k+1 primes for k=0,1,2,...,n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions