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 A226352 Number of integers k in base n whose squared digits sum to sqrt(k). 2
 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, 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, 1, 3, 3, 6, 3, 3, 2, 1, 2, 5, 3, 4, 1, 4, 1, 3, 2, 3, 1 (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. LINKS Christian N. K. Anderson, Table of n, a(n) for n = 2..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. A226353. Cf. A226353, A226224. Cf. digital sums for digits at various powers: A007953, A003132, A055012, A055013, A055014, A055015. Sequence in context: A170822 A054546 A065310 * A238402 A016558 A154395 Adjacent sequences:  A226349 A226350 A226351 * A226353 A226354 A226355 KEYWORD nonn,base AUTHOR Christian N. K. Anderson and Kevin L. Schwartz, Jun 04 2013 STATUS approved

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Last modified May 8 20:32 EDT 2021. Contains 343668 sequences. (Running on oeis4.)