A244282 -id:A244282 - cp's OEIS frontend

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.

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

Offset: 1

Michel Lagneau, Jun 25 2014

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,...

			816 is in the sequence because 81 and 16 are squares.

Cf. A000290, A046030, A244282.

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:

isok(n) = (left = n\10) && issquare(left) && (pt = 10^(#Str(n)-1)) && issquare(n - (n\pt)*pt); \\ Michel Marcus, Jun 25 2014

A244394 Consider a number n with m decimal digits, m>1. The sequence lists the numbers n such that the prefix of length m-1 and the suffix of length m-1 both have the same sum of divisors.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 335, 444, 534, 551, 555, 579, 589, 666, 682, 777, 888, 954, 956, 999, 1102, 1111, 2138, 2204, 2222, 2246, 2649, 3190, 3333, 4354, 4408, 4428, 4444, 5332, 5376, 5555, 5644, 5925, 6294, 6666, 6933, 7480, 7528

Offset: 1

Michel Lagneau, Jun 27 2014

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 sigma(p) = sigma(s) where p is the prefix x(0)x(1)... x(q-1) and s is the suffix x(1)... x(q-1)x(q).

			5376 is in the sequence because sigma(537) = sigma(376) = 720.

Cf. A244282, A244283.

with(numtheory):
for n from 10 to 10000 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:
      x1:=sigma(s1):x2:=sigma(s2):
      if x1 = x2
        then
        printf(`%d, `, n):
        else
      fi:
od:

cp's OEIS Frontend

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.

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