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

1,2

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)

Formula

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

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 *)

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

Crossrefs

Cf. A083114.

Sequence in context: A117055 A117056 A082207 * A266280 A250412 A201060

Adjacent sequences: A083112 A083113 A083114 * A083116 A083117 A083118

Keyword

base,nonn

Author

Amarnath Murthy, Apr 23 2003

Status

approved