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.

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

Author

Hugo Pfoertner, Aug 08 2019

Keywords

• nonn
• base
• hard

Comments

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

Examples

			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.
		

Crossrefs

Cf. A002113, A046385, A046399.

Programs

PARI

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

Extensions

More terms from Giovanni Resta, Aug 08 2019