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 A244283 Consider a number n with m decimal digits, m>9. The sequence lists the numbers n such that the prefix of length m-1 and the suffix of length m-1 are both perfect squares. 3
 10, 11, 14, 19, 40, 41, 44, 49, 90, 91, 94, 99, 164, 364, 649, 816, 1000, 1001, 1004, 1009, 1441, 1961, 2256, 4000, 4001, 4004, 4009, 4841, 6256, 7841, 9000, 9001, 9004, 9009, 20256, 30256, 31369, 40961, 46241, 51849, 54761, 60841, 73969, 79216, 90256, 94096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let x(0)x(1)... x(q-1)x(q) denote the decimal expansion of a number n. The sequence lists the numbers n such that the prefix x(0)x(1)... x(q-1) and the suffix x(1)... x(q-1)x(q) are both a perfect square. The primes of the sequence are 11, 19, 41, 1009, 4001, 7841, 9001, 40961,... LINKS Table of n, a(n) for n=1..46. EXAMPLE 816 is in the sequence because 81 and 16 are squares. MAPLE with(numtheory): for n from 10 to 20000 do: x:=convert(n, base, 10):n1:=nops(x): s1:=sum('x[i]*10^(i-1) ', 'i'=1..n1-1): s2:=(n-irem(n, 10))/10:ss1:=sqrt(s1):ss2:=sqrt(s2): if ss1=floor(ss1) and ss2=floor(ss2) then printf(`%d, `, n): else fi: od: PROG (PARI) isok(n) = (left = n\10) && issquare(left) && (pt = 10^(#Str(n)-1)) && issquare(n - (n\pt)*pt); \\ Michel Marcus, Jun 25 2014 CROSSREFS Cf. A000290, A046030, A244282. Sequence in context: A062844 A144980 A261713 * A373615 A373617 A043583 Adjacent sequences: A244280 A244281 A244282 * A244284 A244285 A244286 KEYWORD nonn,base AUTHOR Michel Lagneau, Jun 25 2014 STATUS approved

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Last modified September 10 03:01 EDT 2024. Contains 375770 sequences. (Running on oeis4.)