A242726 Sphenic numbers k = p*q*r such that reversal(k) is also a sphenic number and reversal(k) = reversal(p)*reversal(q)*reversal(r).

66, 286, 606, 682, 2222, 2486, 2626, 2882, 3333, 3939, 5555, 6262, 6842, 6886, 7777, 9393, 14443, 18887, 22462, 22682, 22826, 24266, 26422, 26462, 26686, 28622, 33693, 34441, 36399, 39633, 39693, 62822, 66242, 68662, 78881, 99363, 118877, 125543, 145541

Offset

1,1

Comments

Subsequence of A007304. A sphenic number is a number that is the product of 3 distinct primes.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2175

Example

3196751 = 31*101*1021 is in the sequence because reversal(3196751) = 1576913 = 13*101*1201 => 31 = reversal(13), 101 = reversal(101) and 1201 = reversal(1021).

Maple

with(numtheory):
for n from 30 to 150000 do :
  x:=factorset(n):n1:=nops(x):
   if bigomega(n)= 3 and n1>2
     then
     y:=convert(n, base, 10):n2:=nops(y):
     p:=x[1]:q:=x[2]:r:=x[3]:
     xp1:=convert(p, base, 10):nxp1:=nops(xp1):
     xq1:=convert(q, base, 10):nxq1:=nops(xq1):
     xr1:=convert(r, base, 10):nxr1:=nops(xr1):
     sp:=sum('xp1[i]*10^(nxp1-i)', 'i'=1..nxp1):
     sq:=sum('xq1[i]*10^(nxq1-i)', 'i'=1..nxq1):
     sr:=sum('xr1[i]*10^(nxr1-i)', 'i'=1..nxr1):
     lst:={sp} union {sq} union {sr}:
     s:=sum('y[i]*10^(n2-i)', 'i'=1..n2):x1:=factorset(s):nn1:=nops(x1):
       if bigomega(s)=3 and nn1>2
         then
         z:=convert(s, base, 10):n3:=nops(z):
         p1:=x1[1]:q1:=x1[2]:r1:=x1[3]:
         lst1:={p1} union {q1} union {r1}:
         s1:=sum('z[i]*10^(n3-i)', 'i'=1..n3):
           if lst = lst1
           then
           printf(`%d, `, n):
           else
           fi:
        fi:
    fi:
  od:

Crossrefs

Cf. A007304, A242592.

Sequence in context: A117306 A322768 A158070 * A271739 A251055 A251048

Adjacent sequences: A242723 A242724 A242725 * A242727 A242728 A242729

Keyword

nonn,base

Author

Michel Lagneau, May 21 2014

Status

approved