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A052061 Numbers n such that decimal expansion of n^2 contains no palindromic substring except single digits. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Leading zeros in substring 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

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

EXAMPLE

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

PROG

(PARI) 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}; n=0; for(n=1, 1e4, if(noPalSub(n^2), print1(n", ")))

CROSSREFS

Cf. A052062, A052063, A052064, A050741.

Sequence in context: A007377 A213882 A135140 * A045540 A119509 A219248

Adjacent sequences:  A052058 A052059 A052060 * A052062 A052063 A052064

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Jan 15 2000.

EXTENSIONS

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

STATUS

approved

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.