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%I #11 Feb 16 2025 08:33:06
%S 8,86,1437,6654,81917,827389,17956860,157286397,1434451965,
%T 12884901885,114353504253,1005022347261,8761733283837,166026255794172,
%U 1337006139375613,11434920928870397,97390341941886973,1799188051134513148,14231374822490767357,119903836479112085501
%N Sum of all n-digit Woodall numbers.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WoodallNumber.html">Woodall Number</a>.
%e Sum of all 1-digit Woodall numbers is 1 + 7 = 8.
%e Sum of all 2-digit Woodall numbers is 23 + 63 = 86.
%e Sum of all 3-digit Woodall numbers is 159 + 383 + 895 = 1437.
%t digNum[n_] := Length @ IntegerDigits[n]; woodall[n_] := n * 2^n - 1; digCount = 0; sum = 0; cumsum = {}; Do[w = woodall[n]; If[digNum[w] > digCount, digCount++; AppendTo[cumsum, sum]]; sum += w, {n, 1, 65}]; Differences[cumsum] (* _Amiram Eldar_, Nov 30 2019 *)
%Y Cf. A003261.
%K nonn,base,less,changed
%O 1,1
%A _Parthasarathy Nambi_, Oct 23 2007
%E More terms from _Amiram Eldar_, Nov 30 2019