|
%I #31 Sep 20 2021 21:29:17
%S 23,22,234,115,1208,212,1269,999,7370,5019,3087,244,2329,2171,147112,
%T 90155,165407,7939,57451,69224,62064,19503,19844,563298,265095,
%U 14759823,121726,167817,97100,808386,7353035,1231680,201722,4754844,91904459
%N Least m such that sqrt(m) has a period 2n continued fraction expansion whose palindrome part concatenates to a palindromic prime.
%C All terms in the palindromic part of the continued fraction expansion of sqrt(a(n)) are themselves palindromes. - _Chai Wah Wu_, Sep 15 2021
%H Chai Wah Wu, <a href="/A072135/b072135.txt">Table of n, a(n) for n = 2..71</a> (terms n = 2..49 from Jon E. Schoenfield)
%H Jon E. Schoenfield, <a href="/A072135/a072135.txt">The continued fraction for each term up through a(49)</a>
%e 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, ...
%Y Cf. A002113, A002385.
%K hard,nice,nonn,base
%O 2,1
%A _Lekraj Beedassy_, Jun 26 2002
%E a(5)-a(36) from _Jon E. Schoenfield_, Apr 02 2010
|
