

A136106


a(n) = smallest prime p such that in the sequence of n numbers p, p+1, p+2, ..., p+n1, the ith term is the product of i distinct primes, for i = 1, ..., n.


1




OFFSET

1,1


LINKS

Table of n, a(n) for n=1..8.


FORMULA

a(n) >= A086560(n).  R. J. Mathar, Feb 05 2008


EXAMPLE

a(4) = 1867 because it begins with the prime 1867 followed by 1868 with two distinct prime factors, 2 and 467; then 1869 with three distinct prime factors, 3, 7 and 89; then 1870 with four distinct prime factors, 2, 5, 11 and 17.


MATHEMATICA

Table[First[Select[Prime@Range@100000, (n=1; k=#; While[Length[First/@FactorInteger@k]==n, k++; n++]; n1==t)&]], {t, 5}] (* Giorgos Kalogeropoulos, May 07 2019 *)


PROG

(PARI) /* a brute force program */ a136106(st, ed, ct)={ forprime(x=st, ed, if ((x%6)!=1, next); goodFlag = 1; c = 1; while(goodFlag, if (!(c%2) && isprime(x+c), goodFlag=0, v = factor(x+c); if (length(v[, 2]) == c+1, c+=1; if (c > ct, print("Level = ", c, " at ", x+c1, "=", v); ct+=1), goodFlag = 0 ) ) ) ); } \\ Fred Schneider, Dec 18 2007


CROSSREFS

Cf. A072875.
Sequence in context: A276267 A215845 A276110 * A122696 A237267 A266284
Adjacent sequences: A136103 A136104 A136105 * A136107 A136108 A136109


KEYWORD

more,nonn


AUTHOR

Enoch Haga, Dec 14 2007


EXTENSIONS

Edited by N. J. A. Sloane, Dec 23 2007
a(5)a(6) from Fred Schneider, Dec 18 2007
a(7) from Donovan Johnson, Sep 19 2009
a(8) from Donovan Johnson, Jul 19 2011


STATUS

approved



