A083115 -id:A083115 - cp's OEIS frontend

A266280 Terms in A083115 that are the smallest members of equivalence classes generated by permutation of digits.

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, 11111, 11211, 11311, 11411, 11511, 11711, 12121, 12221, 13131, 111111, 112211, 1111111, 1112111, 1113111, 1115111, 1121211, 1131311, 11111111, 111111111

Offset: 1

Chai Wah Wu, Dec 27 2015

Subsequence of A083115. Intersection of A083114 and A266140.

Differs from A083115 first at n=27.

Chai Wah Wu, Table of n, a(n) for n = 1..132

Cf. A083114, A083115, A266140.

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

Original entry on oeis.org

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

Amarnath Murthy, Apr 23 2003

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

Cf. A083115.

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 *)

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

Corrected by Harvey P. Dale, Mar 25 2024

cp's OEIS Frontend

A266280 Terms in A083115 that are the smallest members of equivalence classes generated by permutation of digits.

Views

Author

Keywords

Comments

Links

Crossrefs

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions