A050741 -id:A050741 - cp's OEIS frontend

A052061 Numbers k such that decimal expansion of k^2 contains no palindromic substring except single digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 17, 18, 19, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 39, 41, 42, 43, 44, 48, 49, 51, 52, 53, 54, 55, 57, 59, 61, 64, 66, 68, 69, 71, 72, 73, 74, 75, 78, 79, 82, 84, 86, 87, 89, 93, 95, 96, 97, 98, 99, 104, 113, 116, 117, 118, 124

Offset: 1

Patrick De Geest, Jan 15 2000

Leading zeros in the substrings are allowed so 103^2 = 10609 is rejected because 1{060}9 contains a palindromic substring.

Probabilistic analysis strongly suggests that this sequence is not finite. - Franklin T. Adams-Watters, Nov 15 2006

			118^2 = 13924 -> substrings 13, 39, 92, 24, 139, 392, 924, 1392, 3924 and 13924 are all non-palindromic.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10001

Cf. A052062, A052063, A052064, A050741.

noPalSub(n)={my(d);local(digit);digit=eval(Vec(Str(n)));d = #digit;for(len=2,d,for(i=1,d-len+1,if(isPalSub(i,len), return(0))));1};
isPalSub(start,len)={my(b=start-1,e=start+len);for(j=1,len>>1,if(digit[b+j] != digit[e-j], return(0)));1};
for(n=0,200,if(noPalSub(n^2),print1(n", ")))

Program and b-file from Charles R Greathouse IV, Sep 09 2009

A050749 Squares containing no pair of consecutive equal digits.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 169, 196, 256, 289, 324, 361, 484, 529, 576, 625, 676, 729, 784, 841, 961, 1024, 1089, 1296, 1369, 1521, 1681, 1764, 1849, 1936, 2025, 2304, 2401, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3481, 3721, 3969, 4096, 4356

Offset: 1

Patrick De Geest, Sep 15 1999

Intersection of A043096 and A000290.

Cf. A050741.

Select[Range[0,66]^2,FreeQ[Differences[IntegerDigits[#]],0]&] (* Jayanta Basu, May 31 2013 *)
Select[Range[0,100]^2,SequenceCount[IntegerDigits[#],{x_,x_}]==0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 08 2017 *)

a(n) = A050741(n)^2. - Andrew Howroyd, Aug 11 2024

Offset corrected by Andrew Howroyd, Aug 11 2024

A135140 Numbers n such that n and n^2 do not contain successive identical digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 31, 32, 36, 37, 39, 41, 42, 43, 45, 48, 49, 51, 52, 53, 54, 56, 57, 59, 61, 63, 64, 68, 69, 71, 72, 73, 74, 75, 78, 79, 81, 82, 84, 86, 87, 89, 91, 92, 93, 95, 96, 97, 98, 101, 102, 103, 104, 121

Offset: 1

Zak Seidov, Feb 13 2008

G. C. Greubel, Table of n, a(n) for n = 1..1000

A subset of A050741.

Select[Range[0,150],Count[Differences[IntegerDigits[#]],0] == Count[ Differences[IntegerDigits[#^2]],0]==0&] (* Harvey P. Dale, Mar 14 2012 *)

cp's OEIS Frontend

A052061 Numbers k such that decimal expansion of k^2 contains no palindromic substring except single digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions

A050749 Squares containing no pair of consecutive equal digits.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

Extensions

A135140 Numbers n such that n and n^2 do not contain successive identical digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica