A244397 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 have both the same distinct prime divisors.

22, 24, 28, 33, 39, 42, 44, 48, 55, 66, 77, 82, 84, 88, 93, 99, 111, 124, 164, 222, 248, 333, 444, 526, 548, 555, 666, 724, 777, 842, 888, 999, 1111, 1248, 1664, 2162, 2222, 2500, 2855, 3200, 3333, 3600, 3748, 4324, 4444, 4864, 5042, 5128, 5555, 5768, 5882

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 p = x(0)x(1)...x(q-1) and the suffix x(1)...x(q-1)x(q) have the same prime distinct divisors.

Links

Table of n, a(n) for n=1..51.

Example

3748 is in the sequence because 374 and 748 have the same prime divisors: {2,11,17).

Maple

with(numtheory):
for n from 10 to 10000 do:
      x:=convert(n, base, 10):n1:=nops(x):
      s1 := n mod 10^ilog10(n):
      s2:=(n-irem(n, 10))/10:
      x1:=factorset(s1):x2:=factorset(s2):
      if x1 = x2 and x1 <>{}
        then
        printf(`%d, `, n):
        else
      fi:
od:

Crossrefs

Cf. A244394.

Sequence in context: A067189 A030593 A235807 * A138603 A181454 A155911

Adjacent sequences: A244394 A244395 A244396 * A244398 A244399 A244400

Keyword

nonn,base

Author

Michel Lagneau, Jun 27 2014

Status

approved