A083114 Numbers with nonzero digits whose sum of digits as well as product of digits is a palindrome.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 31, 32, 33, 41, 42, 51, 61, 71, 81, 111, 112, 113, 114, 115, 116, 117, 119, 121, 122, 123, 124, 131, 132, 133, 141, 142, 151, 161, 171, 191, 211, 212, 213, 214, 221, 222, 231, 241

Offset: 1

Author

Amarnath Murthy, Apr 23 2003

Keywords

• base
• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..912 (All terms up to 10^7.)

Crossrefs

Cf. A083115.

Programs

Mathematica

id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[x=id[n]]==x; t={}; Do[If[(y=Times@@id[n])>0 && palQ[Plus@@id[n]] && palQ[y],AppendTo[t,n]],{n,222}]; t (* Jayanta Basu, May 15 2013 *)
Select[Range[300],FreeQ[IntegerDigits[#],0]&&AllTrue[{Total[IntegerDigits[#]],Times@@ IntegerDigits[ #]},PalindromeQ]&] (* Harvey P. Dale, Mar 25 2024 *)

PARI

ispal(n)=n=digits(n);for(i=1,#n\2,if(n[i]!=n[#n+1-i],return(0)));1
is(n)=my(d=vecsort(digits(n)));d[1]&&ispal(sum(i=1,#d,d[i]))&&ispal(prod(i=1,#d,d[i])) \\ Charles R Greathouse IV, May 15 2013

Extensions

Corrected by Harvey P. Dale, Mar 25 2024