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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).

%I A242726 #17 Jan 26 2024 04:24:58
%S A242726 66,286,606,682,2222,2486,2626,2882,3333,3939,5555,6262,6842,6886,
%T A242726 7777,9393,14443,18887,22462,22682,22826,24266,26422,26462,26686,
%U A242726 28622,33693,34441,36399,39633,39693,62822,66242,68662,78881,99363,118877,125543,145541
%N 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).
%C A242726 Subsequence of A007304. A sphenic number is a number that is the product of 3 distinct primes.
%H A242726 Chai Wah Wu, <a href="/A242726/b242726.txt">Table of n, a(n) for n = 1..2175</a>
%e A242726 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).
%p A242726 with(numtheory):
%p A242726 for n from 30 to 150000 do :
%p A242726   x:=factorset(n):n1:=nops(x):
%p A242726    if bigomega(n)= 3 and n1>2
%p A242726      then
%p A242726      y:=convert(n,base,10):n2:=nops(y):
%p A242726      p:=x[1]:q:=x[2]:r:=x[3]:
%p A242726      xp1:=convert(p,base,10):nxp1:=nops(xp1):
%p A242726      xq1:=convert(q,base,10):nxq1:=nops(xq1):
%p A242726      xr1:=convert(r,base,10):nxr1:=nops(xr1):
%p A242726      sp:=sum('xp1[i]*10^(nxp1-i)', 'i'=1..nxp1):
%p A242726      sq:=sum('xq1[i]*10^(nxq1-i)', 'i'=1..nxq1):
%p A242726      sr:=sum('xr1[i]*10^(nxr1-i)', 'i'=1..nxr1):
%p A242726      lst:={sp} union {sq} union {sr}:
%p A242726      s:=sum('y[i]*10^(n2-i)', 'i'=1..n2):x1:=factorset(s):nn1:=nops(x1):
%p A242726        if bigomega(s)=3 and nn1>2
%p A242726          then
%p A242726          z:=convert(s,base,10):n3:=nops(z):
%p A242726          p1:=x1[1]:q1:=x1[2]:r1:=x1[3]:
%p A242726          lst1:={p1} union {q1} union {r1}:
%p A242726          s1:=sum('z[i]*10^(n3-i)','i'=1..n3):
%p A242726            if lst = lst1
%p A242726            then
%p A242726            printf(`%d, `,n):
%p A242726            else
%p A242726            fi:
%p A242726         fi:
%p A242726     fi:
%p A242726   od:
%Y A242726 Cf. A007304, A242592.
%K A242726 nonn,base
%O A242726 1,1
%A A242726 _Michel Lagneau_, May 21 2014