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 A226353 Largest integer k in base n whose squared digits sum to sqrt(k). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS 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. LINKS 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. EXAMPLE 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 PROG (R) 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") CROSSREFS Cf. A226352, A226224. Cf. digital sums for digits at various powers: A007953, A003132, A055012, A055013, A055014, A055015. Sequence in context: A134210 A009409 A009431 * A074216 A216870 A254624 Adjacent sequences:  A226350 A226351 A226352 * A226354 A226355 A226356 KEYWORD nonn,base AUTHOR Christian N. K. Anderson and Kevin L. Schwartz, Jun 04 2013 STATUS approved

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Last modified June 16 19:43 EDT 2019. Contains 324155 sequences. (Running on oeis4.)