cp's OEIS Frontend

A226352 Number of integers k in base n whose squared digits sum to sqrt(k).

%I A226352 #16 Feb 01 2020 14:36:22
%S A226352 1,3,2,2,1,1,4,2,1,2,3,6,1,6,3,3,1,2,2,3,2,4,4,4,2,9,2,4,2,3,1,3,3,3,
%T A226352 3,1,2,4,5,4,1,6,1,5,2,5,2,5,4,1,3,5,1,5,2,5,1,7,3,2,2,7,3,2,2,4,3,2,
%U A226352 1,3,3,6,3,3,2,1,2,5,3,4,1,4,1,3,2,3,1
%N A226352 Number of integers k in base n whose squared digits sum to sqrt(k).
%C A226352 Any d-digit number in base n meeting the criterion must also meet the condition d*(n-1)^2 < n^(d/2). Numerically, it can be shown this limits the candidate values to squares < 22*n^4. The larger values are statistically unlikely, and in fact the largest value of k in the first 1000 bases is ~9.96*n^4 in base 775.
%H A226352 Christian N. K. Anderson, <a href="/A226352/b226352.txt">Table of n, a(n) for n = 2..1000</a>
%e A226352 In base 8, the four solutions are the values {1,16,256,2601}, which are written as {1,20,400,5051} in base 8 and
%e A226352 sqrt(1)    =  1 = 1^2;
%e A226352 sqrt(16)   =  4 = 2^2 + 0^2;
%e A226352 sqrt(256)  = 16 = 4^2 + 0^2 + 0^2;
%e A226352 sqrt(2601) = 51 = 5^2 + 0^2 + 5^2 + 1^2,
%o A226352 (R) inbase=function(n, b) { x=c(); while(n>=b) { x=c(n%%b, x); n=floor(n/b) }; c(n, x) }
%o A226352 for(n in 2:50) cat("Base", n, ":", which(sapply((1:(4.7*n^2))^2, function(x) sum(inbase(x, n)^2)==sqrt(x)))^2, "\n")
%Y A226352 Cf. A226353.
%Y A226352 Cf. A226353, A226224.
%Y A226352 Cf. digital sums for digits at various powers: A007953, A003132, A055012, A055013, A055014, A055015.
%K A226352 nonn,base
%O A226352 2,2
%A A226352 _Christian N. K. Anderson_ and _Kevin L. Schwartz_, Jun 04 2013