|
%I #33 Oct 30 2019 01:00:19
%S 7,11,43,139,627,1399,1597,1979,7809,14059,46499
%N Numbers k such that the smoothly undulating palindromic number (4*10^k-7)/33 = 121...21 is a prime (or PRP).
%C Prime versus probable prime status and proofs are given in the author's table.
%C No further terms < 100000. - _Ray Chandler_, Aug 17 2011
%C The corresponding primes, called smoothly undulating palindromic primes (cf. links, A032758 and A059758), are listed in A092696. The number of '12's is given in A056803(n) = (a(n)-1)/2. - _M. F. Hasler_, Jul 30 2015
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 139, p. 48, Ellipses, Paris 2008.
%H P. De Geest, <a href="http://www.worldofnumbers.com/undulat.htm#supp121">SUPP Reference Table - 121</a>
%H <a href="/index/Pri#pri_supp">Index entries for sequences related to smoothly undulating palindromic primes</a>
%e k=11 --> (12*10^11 - 21)/99 = 12121212121.
%t d[n_]:=IntegerDigits[n]; Length/@d[Select[NestList[FromDigits[Join[d[#],{2,1}]]&,1,1000],PrimeQ]] (* _Jayanta Basu_, May 25 2013 *)
%o (PARI) for(n=1,1e5,ispseudoprime(5^n<<(n+2)\33)&&print1(n",")) \\ _M. F. Hasler_, Jul 30 2015
%Y Cf. A062210-A062232, A059758, A032758, A092696, A056803.
%K nonn,base
%O 1,1
%A _Patrick De Geest_ and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001
%E a(11) = 46499 from _Ray Chandler_, Nov 11 2010
%E Edited by _Ray Chandler_, Aug 17 2011
%E Name and other items edited by _M. F. Hasler_, Jul 30 2015
| 