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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.
1
2, 5, 103, 1867, 491851, 17681491, 35565206671, 43194825904693
OFFSET
1,1
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
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