A226352 -id:A226352 - cp's OEIS frontend

A226353 Largest integer k in base n whose squared digits sum to sqrt(k).

1, 49, 169, 36, 1, 1, 2601, 1089, 1, 8836, 33489, 44100, 1, 149769, 128164, 96721, 1, 156816, 1225, 40804, 12321, 831744, 839056, 1149184, 1737124, 3655744, 407044, 1890625, 2208196, 1089, 1, 1466521, 6125625, 2235025, 2832489, 1, 3759721, 6885376, 8844676

Offset: 2

Christian N. K. Anderson and Kevin L. Schwartz, Jun 04 2013

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.

a(n)=1 iff A226352(n)=1.

			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
sqrt(1)   = 1  = 1^2
sqrt(16)  = 4  = 2^2+0^2
sqrt(256) = 16 = 4^2+0^2+0^2
sqrt(2601)= 51 = 5^2+0^2+5^2+1^2

Christian N. K. Anderson, Table of n, a(n) for n = 2..1000
Christian N. K. Anderson, Table of base, all solutions in base 10, and all solutions in base n for bases 2 to 1000.

Cf. A226352, A226224.

Cf. digital sums for digits at various powers: A007953, A003132, A055012, A055013, A055014, A055015.

inbase=function(n,b) { x=c(); while(n>=b) { x=c(n%%b,x); n=floor(n/b) }; c(n,x) }
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")

cp's OEIS Frontend

A226353 Largest integer k in base n whose squared digits sum to sqrt(k).

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