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.
%I A248736 #37 Nov 30 2019 01:32:08
%S A248736 1,1,1,1,1,1,1,1,2,2,1,1,3,4,3,1,2,4,7,8,4,1,2,5,10,15,15,7,1,2,6,14,
%T A248736 25,32,27,10,1,2,7,18,37,58,67,48,15,1,2,8,22,51,94,135,138,86,22,1,2,
%U A248736 9,27,67,140,236,306,280,152,32,1,2,10,32,86,197,377,584,690,565,266,47
%N A248736 Array, read by antidiagonals, of the numbers of digits in the decimal expansion of the number of partitions of b^n employing a conjectured formula. See both the Comments and the Mathematica coding.
%C A248736 This array is based upon the conjectured formula by _Charles R Greathouse IV_ in A077644, adapted to other bases.
%C A248736 As far as the direct computations for bases b = 2..12 and powers n=0..12 cited in cross references are concerned, the values computed here conform to the exact numbers of partitions.
%F A248736 a(b,n) = ceiling(Pi*sqrt(2/3)*sqrt(b)^n - log(48)/2 - n*log b) / log(10).
%e A248736 \n 0 1 2 3 4 5 6 7 8 9 10 11 ...
%e A248736 b\
%e A248736 2 1 1 1 2 3 4 7 10 15 22 32 47
%e A248736 3 1 1 2 4 8 15 27 48 86 152 266 463
%e A248736 4 1 1 3 7 15 32 67 138 280 565 1134 2275
%e A248736 5 1 1 4 10 25 58 135 306 690 1550 3474 7776
%e A248736 6 1 2 5 14 37 94 236 584 1437 3529 8654 21210
%e A248736 7 1 2 6 18 51 140 377 1005 2668 7069 18714 49527
%e A248736 8 1 2 7 22 67 197 565 1607 4555 12898 36494 103238
%e A248736 9 1 2 8 27 86 266 806 2429 7301 21918 65771 197332
%e A248736 10 1 2 9 32 107 347 1108 3515 11132 35219 111391 352269
%e A248736 11 1 2 10 37 130 442 1476 4910 16302 54085 179401 595031
%e A248736 12 1 2 11 43 156 550 1918 6661 23091 80011 277190 960240
%t A248736 f[n_, b_] := Ceiling[(Pi*Sqrt[2/3]*Sqrt[b]^n - Log[48]/2 - n*Log[b]) / Log[10]]; Table[ f[n - b, b], {n, 2, 20}, {b, n, 2, -1}] // Flatten
%t A248736 (* cross checked with *) g[n_, b_] := f[n, b] = Floor[ Log10[ PartitionsP[ b^n]] + 1]; Table[ f[n - b, b], {n, 2, 20}, {b, n, 2, -1}] // Flatten
%Y A248736 Cf. A129490 (row 2), A248729 (row 3), A248731 (row 5), A248733 (row 6), A248735 (row 7), A077644 (row 10).
%K A248736 nonn,base,tabl
%O A248736 1,9
%A A248736 _Robert G. Wilson v_, Oct 12 2014