A083115 Palindromes in A083114.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 111, 121, 131, 141, 151, 161, 171, 191, 212, 222, 313, 1111, 1221, 1331, 2112, 3113, 11111, 11211, 11311, 11411, 11511, 11711, 12121, 12221, 13131, 21112, 21212, 31113, 111111, 112211, 121121

Offset: 1

Author

Amarnath Murthy, Apr 23 2003

Keywords

• base
• nonn

Comments

Intersection of A117056 and A052382. - Jayanta Basu, May 15 2013

Links

• Charles R Greathouse IV and Chai Wah Wu, Table of n, a(n) for n = 1..2002 (n = 1..59 from Charles R Greathouse IV)

Crossrefs

Cf. A083114.

Programs

Mathematica

id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[x=id[n]]==x; t={}; Do[If[palQ[n] && (y=Times@@id[n])>0 && palQ[Plus@@id[n]] && palQ[y],AppendTo[t,n]],{n,125000}]; t (* Jayanta Basu, May 15 2013 *)
spQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&AllTrue[ {n,Total[ idn],Times@@idn},PalindromeQ]]; Select[Range[125000],spQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 30 2021 *)

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]))&&ispal(n) \\ Charles R Greathouse IV, May 15 2013

Formula

a(n) >> 3^n. - Charles R Greathouse IV, May 15 2013