login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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