The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A083140 Sieve of Eratosthenes arranged as an array and read by antidiagonals in the up direction; n-th row has property that smallest prime factor is prime(n). 48
 2, 3, 4, 5, 9, 6, 7, 25, 15, 8, 11, 49, 35, 21, 10, 13, 121, 77, 55, 27, 12, 17, 169, 143, 91, 65, 33, 14, 19, 289, 221, 187, 119, 85, 39, 16, 23, 361, 323, 247, 209, 133, 95, 45, 18, 29, 529, 437, 391, 299, 253, 161, 115, 51, 20, 31, 841, 667, 551, 493, 377, 319, 203, 125, 57, 22 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS A permutation of natural numbers >= 2. The proportion of integers in the n-th row of the array is given by A005867(n-1)/A002110(n) = A038110(n)/A038111(n). - Peter Kagey, Jun 03 2019, based on comments by Jamie Morken and discussion with Tom Hanlon. The proportion of the integers after the n-th row of the array is given by A005867(n)/A002110(n). - Tom Hanlon, Jun 08 2019 LINKS Ivan Neretin, Table of n, a(n) for n = 2..5051 EXAMPLE Array begins:    2   4   6   8  10  12  14  16  18  20  22  24 .... (A005843 \ {0})    3   9  15  21  27  33  39  45  51  57  63  69 .... (A016945)    5  25  35  55  65  85  95 115 125 145 155 175 .... (A084967)    7  49  77  91 119 133 161 203 217 259 287 301 .... (A084968)   11 121 143 187 209 253 319 341 407 451 473 517 .... (A084969)   13 169 221 247 299 377 403 481 533 559 611 689 .... (A084970) MATHEMATICA a = Join[ {Table[2n, {n, 1, 12}]}, Table[ Take[ Prime[n]*Select[ Range, GCD[ Prime[n] #, Product[ Prime[i], {i, 1, n - 1}]] == 1 &], 12], {n, 2, 12}]]; Flatten[ Table[ a[[i, n - i]], {n, 2, 12}, {i, n - 1, 1, -1}]] (* second program: *) rows = 12; Clear[T]; Do[For[m = p = Prime[n]; k = 1, k <= rows, m += p, If[ FactorInteger[m][[1, 1]] == p, T[n, k++] = m]], {n, rows}]; Table[T[n - k + 1, k], {n, rows}, {k, n}] // Flatten (* Jean-François Alcover, Mar 08 2016 *) CROSSREFS Cf. A083141 (main diagonal), A083221 (transpose), A004280, A038179, A084967, A084968, A084969, A084970, A084971. Arrays of integers grouped into rows by various criteria: by greatest prime factor: A125624, by lowest prime factor: this sequence (upward antidiagonals), A083221 (downward antidiagonals), by number of distinct prime factors: A125666, by number of prime factors counted with multiplicity: A078840, by prime signature: A095904, by ordered prime signature: A096153, by number of divisors: A119586, by number of 1's in binary expansion: A066884 (upward), A067576 (downward), by distance to next prime: A192179. Cf. A002110, A005867, A038110, A038111. Sequence in context: A119586 A095904 A096153 * A246279 A285112 A253565 Adjacent sequences:  A083137 A083138 A083139 * A083141 A083142 A083143 KEYWORD nonn,tabl,nice AUTHOR Yasutoshi Kohmoto, Jun 05 2003 EXTENSIONS More terms from Hugo Pfoertner and Robert G. Wilson v, Jun 13 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 7 19:14 EDT 2020. Contains 335498 sequences. (Running on oeis4.)