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A113470 Triangle read by rows: n-th row is the smallest set of n numbers in arithmetic progression with the same number of divisors. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 16 12:16 EDT 2021. Contains 343942 sequences. (Running on oeis4.)