cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A325277 Irregular triangle read by rows where row 1 is {1} and row n is the sequence starting with n and repeatedly applying A181819 until a prime number is reached.

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%I A325277 #7 Apr 16 2019 15:27:11
%S A325277 1,2,3,4,3,5,6,4,3,7,8,5,9,3,10,4,3,11,12,6,4,3,13,14,4,3,15,4,3,16,7,
%T A325277 17,18,6,4,3,19,20,6,4,3,21,4,3,22,4,3,23,24,10,4,3,25,3,26,4,3,27,5,
%U A325277 28,6,4,3,29,30,8,5,31,32,11,33,4,3
%N A325277 Irregular triangle read by rows where row 1 is {1} and row n is the sequence starting with n and repeatedly applying A181819 until a prime number is reached.
%C A325277 The function A181819 maps p^i*...*q^j to prime(i)*...*prime(j) where p through q are distinct primes.
%F A325277 T(n,k) = A325239(n,k) for k <= A323014(n).
%F A325277 A001222(T(n,k)) = A323023(n,k) for n > 1.
%e A325277 Triangle begins:
%e A325277    1            26 4 3        51 4 3          76 6 4 3
%e A325277    2            27 5          52 6 4 3        77 4 3
%e A325277    3            28 6 4 3      53              78 8 5
%e A325277    4 3          29            54 10 4 3       79
%e A325277    5            30 8 5        55 4 3          80 14 4 3
%e A325277    6 4 3        31            56 10 4 3       81 7
%e A325277    7            32 11         57 4 3          82 4 3
%e A325277    8 5          33 4 3        58 4 3          83
%e A325277    9 3          34 4 3        59              84 12 6 4 3
%e A325277   10 4 3        35 4 3        60 12 6 4 3     85 4 3
%e A325277   11            36 9 3        61              86 4 3
%e A325277   12 6 4 3      37            62 4 3          87 4 3
%e A325277   13            38 4 3        63 6 4 3        88 10 4 3
%e A325277   14 4 3        39 4 3        64 13           89
%e A325277   15 4 3        40 10 4 3     65 4 3          90 12 6 4 3
%e A325277   16 7          41            66 8 5          91 4 3
%e A325277   17            42 8 5        67              92 6 4 3
%e A325277   18 6 4 3      43            68 6 4 3        93 4 3
%e A325277   19            44 6 4 3      69 4 3          94 4 3
%e A325277   20 6 4 3      45 6 4 3      70 8 5          95 4 3
%e A325277   21 4 3        46 4 3        71              96 22 4 3
%e A325277   22 4 3        47            72 15 4 3       97
%e A325277   23            48 14 4 3     73              98 6 4 3
%e A325277   24 10 4 3     49 3          74 4 3          99 6 4 3
%e A325277   25 3          50 6 4 3      75 6 4 3       100 9 3
%t A325277 red[n_]:=Times@@Prime/@Last/@If[n==1,{},FactorInteger[n]];
%t A325277 Table[NestWhileList[red,n,#>1&&!PrimeQ[#]&],{n,30}]
%Y A325277 Row lengths are 1 for n = 1 and A323014(n) for n > 1.
%Y A325277 Cf. A001221, A001222, A071625, A118914, A181819, A181821, A182850, A182857, A323022, A323023, A325238, A325239.
%K A325277 nonn,tabf
%O A325277 1,2
%A A325277 _Gus Wiseman_, Apr 15 2019