A113470 Triangle read by rows: n-th row is the smallest set of n numbers in arithmetic progression with the same number of divisors.

1, 2, 3, 3, 5, 7, 5, 11, 17, 23, 5, 11, 17, 23, 29, 7, 37, 67, 97, 127, 157, 35, 65, 95, 125, 155, 185, 215, 635, 707, 779, 851, 923, 995, 1067, 1139, 635, 707, 779, 851, 923, 995, 1067, 1139, 1211, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089, 3841, 3973

Offset

1,2

Comments

In this sequence "smallest" means that the last term of the arithmetic progression is minimized and if there is still a choice then we minimize the common difference of the arithmetic progression.

Links

Table of n, a(n) for n=1..57.

OEIS wiki, Primes in arithmetic progression.

Formula

T(n,k) = A090547(n) + (k-1)*A090549(n). - R. J. Mathar, May 11 2007

Example

From M. F. Hasler, Jan 02 2020: (Start)
The triangle starts
    n | row n
   ---+------------
    1 |    1,
    2 |    2,    3,
    3 |    3,    5,    7,
    4 |    5,   11,   17,   23,
    5 |    5,   11,   17,   23,   29,
    6 |    7,   37,   67,   97,  127,  157,
    7 |   35,   65,   95,  125,  155,  185,  215,
    8 |  635,  707,  779,  851,  923,  995, 1067, 1139,
    9 |  635,  707,  779,  851,  923,  995, 1067, 1139, 1211,
   10 |  199,  409,  619,  829, 1039, 1249, 1459, 1669, 1879, 2089,
   11 | 3841, 3973,  ...
Most rows so far consist of primes with 2 divisors, rows 7, 8, 9 and 11 have squarefree semiprimes with 4 divisors.
Row 10 is A033168; also row 10 of A086786, A133276 and A133277. (End)

Crossrefs

Cf. A086786, A090547, A090548, A090549.

Sequence in context: A084127 A089934 A113460 * A086786 A211890 A231406

Adjacent sequences: A113467 A113468 A113469 * A113471 A113472 A113473

Keyword

nonn,tabl

Author

David Wasserman, Jan 08 2006

Status

approved