A046399
Smallest squarefree palindrome with exactly n distinct prime factors.
Original entry on oeis.org
1, 2, 6, 66, 858, 6006, 222222, 22444422, 244868442, 6434774346, 438024420834, 50146955964105, 2415957997595142, 495677121121776594, 22181673755737618122, 5521159517777159511255, 477552751050050157255774
Offset: 0
- J.-P. Delahaye, Merveilleux nombres premiers ("Amazing primes"), p. 315, Pour la Science, Paris 2000.
-
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 *)
A309565
Least base-10 palindrome whose factorization includes an arbitrary number m of prime factors, with n <= m of them, all counted with multiplicity, being base-10 palindromes.
Original entry on oeis.org
1, 2, 4, 8, 88, 252, 2772, 29792, 2112, 4224, 8448, 489984, 48384, 2977792, 8634368, 405504, 40955904, 405909504, 23080108032, 25135153152, 677707776, 2557800087552, 21128282112, 633498894336, 23255666655232, 8691508051968, 29142024192, 65892155129856, 4815463645184
Offset: 0
a(7) = 29792 because it is the smallest number that has a factorization 2^5 * 7^2 * 19 including 7 palindromic prime factors: 2, 2, 2, 2, 2, 7, 7.
A046385(7) = 82728 = 2^3 * 3^3 * 383 is the smallest number with 7 palindromic prime factors and no non-palindromic prime factors.
a(20) = A046385(20) = 677707776 = 2^16 * 3^3 * 383.
-
is_A002113(n)={Vecrev(n=digits(n))==n};
haspalf(P)={my(x=factor(P),nf=#x[,2],m=0);for(j=1,nf,if(is_A002113(x[j,1]),m+=x[j,2]));m};
for(d=1,16,for(k=1,oo,if(is_A002113(k),if(haspalf(k)==d,print1(k,", ");break)))) \\ Hugo Pfoertner, Aug 08 2019 using is_A002113 by M. F. Hasler
A335934
Smallest palindrome in base 10 whose factorization contains n distinct base 10 palindromic prime factors.
Original entry on oeis.org
1, 2, 6, 66, 2772, 279972, 67566576, 5159488849515, 83797355379738
Offset: 0
a(6) = 67566576 = 2^4*3*7*11*101*181 has 6 distinct palindromic prime factors.
Showing 1-3 of 3 results.
Comments