A113548 Least non-palindromic number k such that k and its digital reversal both have exactly n prime divisors.

13, 12, 132, 1518, 15015, 204204, 10444434, 241879638, 20340535215, 242194868916, 136969856585562, 2400532020354468, 484576809394483806, 200939345091539746692

Offset

1,1

Comments

This sequence does not allow ending in 0, else a(8) = 208888680, a(11) = 64635504163230 and a(13) = 477566276048801940. - Michael S. Branicky, Feb 14 2023

Links

Table of n, a(n) for n=1..14.

Formula

a(n) >= A239696(n). - Daniel Suteu, Feb 18 2023

Example

a(1)=13=13 since 31=31,
a(2)=12=2^2*3 since 21=3*7,
a(3)=132=2^2*3*11 since 231=3*7*11,
...
a(7)=10444434=2*3*7*11*13*37*47 since 43444401=3*7*11*13*17*23*37,
a(8)=241879638=2*3*7*11*13*17*23*103 since 836978142=2*3*7*11*13*23*73*83.

Mathematica

r[n_] := FromDigits[ Reverse[ IntegerDigits[ n]]]; f[n_] := Block[{k = r[n], len = Length[ FactorInteger[n]]}, If[k != n && len == Length[ FactorInteger[ r[n]]], len, 0]]; t = Table[0, {10}]; Do[ a = f[n]; If[a > 0 && t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 107}]; t

Prog

(PARI)
generate(A, B, n) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), if(q==5 && m%2==0, next); my(v=m*q); while(v <= B, if(j==1, my(r=fromdigits(Vecrev(digits(v)))); if(v>=A && r != v && omega(r) == n, listput(list, v)), if(v*(q+1) <= B, list=concat(list, f(v, q+1, j-1)))); v *= q)); list); vecsort(Vec(f(1, 2, n)));
a(n) = my(x=vecprod(primes(n)), y=2*x); while(1, my(v=generate(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Feb 18 2023

Crossrefs

Cf. A110843, A110819, A239696.

Sequence in context: A212526 A019331 A004454 * A249998 A195210 A175850

Adjacent sequences: A113545 A113546 A113547 * A113549 A113550 A113551

Keyword

base,hard,nonn

Author

Ryan Propper and Robert G. Wilson v, Sep 21 2005

Extensions

Edited and extended by Giovanni Resta, Jan 16 2006

a(9)-a(10) from Giovanni Resta, Feb 23 2014

a(11)-a(13) from Michael S. Branicky, Feb 14 2023

a(14) from Daniel Suteu, Feb 18 2023

Status

approved