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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 June 19 19:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)