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

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

1,2

Links

Table of n, a(n) for n=1..28.

Index entries for sequences related to primes in arithmetic progressions

Formula

T(n, k) = A034173(n) - 1 + k = A034174(n) - n + k (which implies T(n, k+1) = T(n, k)+1 for k < n) for all 1 <= k <= n >= 1. - M. F. Hasler, Apr 27 2026

Example

Triangle begins:
          1
          2         3
         33        34        35
      19940     19941     19942     19943
     204323    204324    204325    204326    204327
  380480345 380480346 380480347 380480348 380480349 380480350
  ...

Prog

(PARI) A083785(n, k)=A034173(n)+k-1 \\ M. F. Hasler, Apr 27 2026

Crossrefs

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

Cf. A034173, A034174, A083787.

Sequence in context: A358041 A066269 A376557 * A046487 A062922 A080471

Adjacent sequences: A083782 A083783 A083784 * A083786 A083787 A083788

Keyword

nonn,tabl,nice

Author

Amarnath Murthy, May 07 2003

Extensions

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

Status

approved