The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182944 Square array A(i,j), i >= 1, j >= 1, of prime powers prime(i)^j, by descending antidiagonals. 12
 2, 4, 3, 8, 9, 5, 16, 27, 25, 7, 32, 81, 125, 49, 11, 64, 243, 625, 343, 121, 13, 128, 729, 3125, 2401, 1331, 169, 17, 256, 2187, 15625, 16807, 14641, 2197, 289, 19, 512, 6561, 78125, 117649, 161051, 28561, 4913, 361, 23 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS We alternatively refer to this sequence as a triangle T(.,.), with T(n,k) = A(k,n-k+1) = prime(k)^(n-k+1). The monotonic ordering of this sequence, prefixed by 1, is A000961. The joint-rank array of this sequence is A182869. Main diagonal gives A062457. - Omar E. Pol, Sep 11 2018 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1..150, flattened) Michael De Vlieger, Diagram showing row n of triangle in a semicircle as noted, with a color function associated with the magnitude of T(n,k) compared to 2^n in light blue, where prime(n) is the smallest and the prime power indicated in red the largest in the row. FORMULA From Peter Munn, Dec 29 2019: (Start) A(i,j) = A182945(j,i) = A319075(j,i). A(i,j) = A242378(i-1,2^j) = A329332(2^(i-1),j). A(i,i) = A062457(i). (End) EXAMPLE Square array A(i,j) begins: i \ j: 1 2 3 4 5 ... ---\------------------------------------- 1: 2, 4, 8, 16, 32, ... 2: 3, 9, 27, 81, 243, ... 3: 5, 25, 125, 625, 3125, ... 4: 7, 49, 343, 2401, 16807, ... ... The triangle T(n,k) begins: n\k: 1 2 3 4 5 6 ... 1: 2 2: 4 3 3: 8 9 5 4: 16 27 25 7 5: 32 81 125 49 11 6: 64 243 625 343 121 13 ... MATHEMATICA TableForm[Table[Prime[n]^j, {n, 1, 14}, {j, 1, 8}]] CROSSREFS Cf. A000961, A006939 (row products of triangle), A062457, A182945, A332979 (row maxima of triangle). Columns: A000040 (1), A001248 (2), A030078 (3), A030514 (4), A050997 (5), A030516 (6), A092759 (7), A179645 (8), A179665 (9), A030629 (10). A319075 extends the array with 0th powers. Subtable of A242378, A284457, A329332. Sequence in context: A269851 A284457 A365656 * A269385 A252755 A366275 Adjacent sequences: A182941 A182942 A182943 * A182945 A182946 A182947 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 14 2010 EXTENSIONS Clarified in respect of alternate reading as a triangle by Peter Munn, Aug 28 2022 STATUS approved

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

Last modified April 18 18:58 EDT 2024. Contains 371781 sequences. (Running on oeis4.)