[ May 1, 2022 ]
Operations with nine- & pandigital factors creating palindromes
Alexandru Petrescu

There are 8 solutions for the pandigitals and only one for the ninedigitals.
Note the two pandigital duplicates (#2 & #6) and (#7 & #8).

#	Ninedigital	Sum	Product
1	749813526	2+3+7+11+17+263 = 303	2*3*7*11*17*263 = 2065602
#	Pandigital	Sum	Product
1	1854906237	3+37+283 = 323	3*37*283 = 31413
2	1957860432	2+3+11+499+2477 = 2992	2*3*11*499*2477 = 81577518
3	2589361047	3+7+13+37+313 = 373	3*7*13*37*313 = 3161613
4	2943816507	3+43+61+197+211 = 515	3*43*61*197*211 = 327090723
5	3169540287	3+37+101+283 = 424	3*37*101*283 = 3172713
6	3915720864	2+3+11+499+2477 = 2992	2*3*11*499*2477 = 81577518
7	4357812096	2+3+11+17+613 = 646	2*3*11*17*613 = 687786
8	7130965248	2+3+11+17+613 = 646	2*3*11*17*613 = 687786

Here is some Pari/gp code to reproduce Alexandru's results.

{
for(n=1,10!, d=numtoperm(10, n+10!-1);
a=sum(i=1, #d, (d[i]-1)*10^(#d-i));
f=factor(a); sf=0; mf=1;
for(j=1,#f~, sf+=f[j,1]; mf*=f[j,1]);
dsf=digits(sf); dmf=digits(mf); 
if(Vecrev(dsf)==dsf && Vecrev(dmf)==dmf,
print(a," ",f," sum = ",sf,", product = ",mf));
);
}