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A136106 a(n) = smallest prime p such that in the sequence of n numbers p, p+1, p+2, ..., p+n-1, the i-th term is the product of i distinct primes, for i = 1, ..., n. 1
2, 5, 103, 1867, 491851, 17681491, 35565206671, 43194825904693 (list; graph; refs; listen; history; text; internal format)
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++]; n-1==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+c-1, "=", 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

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Last modified December 1 08:58 EST 2022. Contains 358467 sequences. (Running on oeis4.)