A046394 -id:A046394 - cp's OEIS frontend

A046399 Smallest squarefree palindrome with exactly n distinct prime factors.

1, 2, 6, 66, 858, 6006, 222222, 22444422, 244868442, 6434774346, 438024420834, 50146955964105, 2415957997595142, 495677121121776594, 22181673755737618122, 5521159517777159511255, 477552751050050157255774

Offset: 0

Patrick De Geest, Jun 15 1998

Initial terms of sequences A046392-A046398.

			a(4) = 858 = 2*3*11*13.

J.-P. Delahaye, Merveilleux nombres premiers ("Amazing primes"), p. 315, Pour la Science, Paris 2000.

Cf. A046385, A076886.

Cf. A046392, A046393, A046394, A046395, A046396, A046397, A046398.

r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[k = 1; While[r[k] != k || !SquareFreeQ[k] || Length[Select[Divisors[k], PrimeQ]] != n, k++ ]; Print[k], {n, 0, 30}] (* Ryan Propper, Sep 16 2005 *)

Edited by N. J. A. Sloane, Dec 06 2008 at the suggestion of R. J. Mathar
a(10)-a(13) from Donovan Johnson, Oct 03 2011
a(14)-a(15) from David A. Corneth, Oct 03 2020
a(15) corrected by Daniel Suteu, Feb 05 2023
a(16) from Michael S. Branicky, Feb 08 2023

A356767 Tetraprimes (products of four distinct primes) whose reversals are different tetraprimes.

Original entry on oeis.org

1518, 2046, 2226, 2262, 2418, 2478, 2618, 2622, 2814, 2838, 2886, 3135, 3927, 4170, 4182, 4386, 4389, 4746, 4785, 4935, 5313, 5394, 5406, 5478, 5565, 5655, 5838, 5874, 6018, 6045, 6222, 6402, 6438, 6474, 6486, 6690, 6699, 6834, 6846, 6882, 7293, 7458, 8106, 8142

Offset: 1

Tanya Khovanova, Aug 26 2022

Palindromic tetraprimes are A046394.

The corresponding sequence for three distinct primes is A270175.

			1518 = 2*3*11*23 is a tetraprime. Its reversal 8151 = 3*11*13*19 is another tetraprime. Thus, 1518 is in this sequence.

Cf. A046394, A270175.

Select[Range[10000],Transpose[ FactorInteger[FromDigits[Reverse[IntegerDigits[#]]]]][[2]] == {1, 1, 1, 1} && IntegerDigits[#] != Reverse[IntegerDigits[#]] && Transpose[FactorInteger[#]][[2]] == {1, 1, 1, 1} &]

from sympy import factorint
def tetra(n): return list(factorint(n).values()) == [1, 1, 1, 1]
def ok(n):
    if not tetra(n): return False
    revn = int(str(n)[::-1])
    return n != revn and tetra(revn)
print([k for k in range(9000) if ok(k)]) # Michael S. Branicky, Aug 27 2022

cp's OEIS Frontend

A046399 Smallest squarefree palindrome with exactly n distinct prime factors.

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