A072135 Least m such that sqrt(m) has a period 2n continued fraction expansion whose palindrome part concatenates to a palindromic prime.

23, 22, 234, 115, 1208, 212, 1269, 999, 7370, 5019, 3087, 244, 2329, 2171, 147112, 90155, 165407, 7939, 57451, 69224, 62064, 19503, 19844, 563298, 265095, 14759823, 121726, 167817, 97100, 808386, 7353035, 1231680, 201722, 4754844, 91904459

Offset

2,1

Comments

All terms in the palindromic part of the continued fraction expansion of sqrt(a(n)) are themselves palindromes. - Chai Wah Wu, Sep 15 2021

Links

Chai Wah Wu, Table of n, a(n) for n = 2..71 (terms n = 2..49 from Jon E. Schoenfield)

Jon E. Schoenfield, The continued fraction for each term up through a(49)

Example

23 is in the sequence because it is the first, followed by 47, 96, 98, 119, 128, ... all exhibiting the following property: sqrt(23) = [4; 1, 3, 1, 8], sqrt(47) = [6; 1, 5, 1, 12], sqrt(96) = [9; 1, 3, 1, 18], sqrt(98) = [9; 1, 8, 1, 18], sqrt(119) = [10; 1, 9, 1, 20], sqrt(128) = [11; 3, 5, 3, 22], ... i.e., the continued fraction expansion of their square roots have palindrome parts which concatenate respectively to the 3-digit palprimes 131, 151, 131, 181, 191, 353, ...

Crossrefs

Cf. A002113, A002385.

Sequence in context: A255228 A374669 A255221 * A204633 A010862 A291570

Adjacent sequences: A072132 A072133 A072134 * A072136 A072137 A072138

Keyword

hard,nice,nonn,base

Author

Lekraj Beedassy, Jun 26 2002

Extensions

a(5)-a(36) from Jon E. Schoenfield, Apr 02 2010

Status

approved