A309565 - OEIS

%I #10 Aug 08 2019 09:31:19

%S 1,2,4,8,88,252,2772,29792,2112,4224,8448,489984,48384,2977792,

%T 8634368,405504,40955904,405909504,23080108032,25135153152,677707776,

%U 2557800087552,21128282112,633498894336,23255666655232,8691508051968,29142024192,65892155129856,4815463645184

%N 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.

%C Similar to A046385, which excludes prime factors that are not base-10 palindromes, i.e. m = n.

%e 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.

%e A046385(7) = 82728 = 2^3 * 3^3 * 383 is the smallest number with 7 palindromic prime factors and no non-palindromic prime factors.

%e a(20) = A046385(20) = 677707776 = 2^16 * 3^3 * 383.

%o (PARI) is_A002113(n)={Vecrev(n=digits(n))==n};

%o 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};

%o 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_

%Y Cf. A002113, A046385, A046399.

%K nonn,base,hard

%O 0,2

%A _Hugo Pfoertner_, Aug 08 2019

%E More terms from _Giovanni Resta_, Aug 08 2019