A083114 - OEIS

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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

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OFFSET

1,2

LINKS

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

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 *)

PROG

(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

CROSSREFS

Cf. A083115.

Sequence in context: A167619 A020664 A055570 * A129350 A368365 A004746

Adjacent sequences: A083111 A083112 A083113 * A083115 A083116 A083117

KEYWORD

base,easy,nonn

AUTHOR

Amarnath Murthy, Apr 23 2003

EXTENSIONS

Corrected by Harvey P. Dale, Mar 25 2024

STATUS

approved