A062209 Numbers k such that the smoothly undulating palindromic number (4*10^k-7)/33 = 121...21 is a prime (or PRP).

7, 11, 43, 139, 627, 1399, 1597, 1979, 7809, 14059, 46499

Offset

1,1

Comments

Prime versus probable prime status and proofs are given in the author's table.

No further terms < 100000. - Ray Chandler, Aug 17 2011

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

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 139, p. 48, Ellipses, Paris 2008.

Links

Table of n, a(n) for n=1..11.

P. De Geest, SUPP Reference Table - 121

Index entries for sequences related to smoothly undulating palindromic primes

Example

k=11 --> (12*10^11 - 21)/99 = 12121212121.

Mathematica

d[n_]:=IntegerDigits[n]; Length/@d[Select[NestList[FromDigits[Join[d[#], {2, 1}]]&, 1, 1000], PrimeQ]] (* Jayanta Basu, May 25 2013 *)

Prog

(PARI) for(n=1, 1e5, ispseudoprime(5^n<<(n+2)\33)&&print1(n", ")) \\ M. F. Hasler, Jul 30 2015

Crossrefs

Cf. A062210-A062232, A059758, A032758, A092696, A056803.

Sequence in context: A268579 A129865 A153377 * A086828 A117392 A105867

Adjacent sequences: A062206 A062207 A062208 * A062210 A062211 A062212

Keyword

nonn,base

Author

Patrick De Geest and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001

Extensions

a(11) = 46499 from Ray Chandler, Nov 11 2010

Edited by Ray Chandler, Aug 17 2011

Name and other items edited by M. F. Hasler, Jul 30 2015

Status

approved