A083787 -id:A083787 - cp's OEIS frontend

A034174 a(n) is minimal such that prime factorizations of a(n)-n+1, ..., a(n) have same exponents.

1, 3, 35, 19943, 204327, 380480350, 440738966079

Offset: 1

Dean Hickerson, Oct 01 1998

The final terms of the arithmetic progressions defined in A083785. - N. J. A. Sloane, Oct 18 2007
a(8) > 10^13. - Donovan Johnson, Oct 20 2009. [See Reble link for an upper limit.]
The main entry is A034173, which should be updated whenever something relevant is added here. - M. F. Hasler, Oct 28 2012

			a(4)=19943 because 19940, ..., 19943 all have the form p^2 q r.

Don Reble, A034173(8) exists, SeqFan list, Oct 23 2012
Index entries for sequences related to primes in arithmetic progressions

Diagonal of A083785. Cf. A034173, A083785, A083787. See A034173 for more.

A034174(n)={my(f); for(k=n, oo, f=0; for(i=0, n-1, f==(f=vecsort(factor(k-i)[, 2])) || !i || [k+=n-i-1; next(2)]); return(k))} \\ For illustrative purpose; not useful for n>=6. - M. F. Hasler, Oct 28 2012

a(n) = A034173(n) + n - 1. - Max Alekseyev, Nov 10 2009

a(7) from Donovan Johnson, Oct 20 2009

A083785 Triangle read by rows in which the n-th row gives the smallest set of n consecutive numbers with the same prime signatures.

Original entry on oeis.org

1, 2, 3, 33, 34, 35, 19940, 19941, 19942, 19943, 204323, 204324, 204325, 204326, 204327, 380480345, 380480346, 380480347, 380480348, 380480349, 380480350, 440738966073, 440738966074, 440738966075, 440738966076, 440738966077, 440738966078, 440738966079

Offset: 1

Amarnath Murthy, May 07 2003

			       1
       2      3
      33     34     35
   19940  19941  19942  19943
  204323 204324 204325 204326 204327
  ...

Index entries for sequences related to primes in arithmetic progressions

The first column is given by A034173, the final terms by A034174.

Cf. A034173, A034174, A083787.

7th row added using A034173 by Michel Marcus, Dec 13 2015

cp's OEIS Frontend

A034174 a(n) is minimal such that prime factorizations of a(n)-n+1, ..., a(n) have same exponents.

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