A136106 a(n) is the smallest prime p such that in the sequence of n numbers p, p+1, p+2, ..., p+n-1, the i-th term has exactly i distinct prime factors, for i = 1, ..., n.

2, 5, 103, 1867, 491851, 17681491, 35565206671, 43194825904693

Offset

1,1

Links

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

Formula

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

A001221(a(n)+k) = k+1 for 0 <= k <= n-1. - Pontus von Brömssen, Jan 09 2023

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. A001221, A072875, A086560.

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

Name clarified by Pontus von Brömssen, Jan 09 2023

Status

approved