cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 24 results. Next

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

Original entry on oeis.org

7, 11, 43, 139, 627, 1399, 1597, 1979, 7809, 14059, 46499
Offset: 1

Views

Author

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

Keywords

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

Examples

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

References

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

Links

Crossrefs

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

Programs

  • Mathematica
    d[n_]:=IntegerDigits[n]; Length/@d[Select[NestList[FromDigits[Join[d[#],{2,1}]]&,1,1000],PrimeQ]] (* Jayanta Basu, May 25 2013 *)
  • PARI
    for(n=1,1e5,ispseudoprime(5^n<<(n+2)\33)&&print1(n",")) \\ M. F. Hasler, Jul 30 2015

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

A077799 Numbers m such that a smoothly undulating palindromic prime of the form (rs*10^m-sr)/99 exists, where r and s are two distinct digits and rs and sr denote concatenations of those digits.

Original entry on oeis.org

3, 5, 7, 9, 11, 15, 17, 21, 23, 25, 27, 31, 33, 37, 39, 43, 45, 51, 55, 57, 63, 65, 71, 77, 81, 83, 89, 95, 99, 109, 133, 139, 143, 145, 149, 161, 163, 195, 209, 219, 225, 229, 237, 243, 245, 277, 315, 357, 479, 513, 515, 537, 551, 561, 567, 583, 627, 849, 857
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

Edited by Ray Chandler, Aug 17 2011
Name clarified by Sean A. Irvine, Jun 14 2025

A062210 Numbers k such that the smoothly undulating palindromic number (14*10^k - 41)/99 is a prime.

Original entry on oeis.org

11, 277, 479, 583, 1631, 6343, 14689
Offset: 1

Views

Author

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

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			11 is in the sequence because (14*10^11 - 41)/99 = 14141414141 is prime.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

Edited by Ray Chandler, Aug 17 2011
Name and Example edited by Jon E. Schoenfield, Jun 25 2017

A062216 Numbers k such that the smoothly undulating palindromic number (31*10^k - 13)/99 is a prime.

Original entry on oeis.org

3, 51, 83, 225, 561, 10419, 18255, 43869
Offset: 1

Views

Author

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

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=51 -> (31*10^51 - 13)/99 = 313131313131313131313131313131313131313131313131313.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

43869 from Ray Chandler, Sep 30 2010
Edited by Ray Chandler, Aug 17 2011

A062220 Numbers k such that the smoothly undulating palindromic number (38*10^k - 83)/99 is a prime.

Original entry on oeis.org

3, 9, 15, 17, 21, 57, 4233, 4335, 13221, 26447, 29897, 91997
Offset: 1

Views

Author

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

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=21 -> (38*10^21 - 83)/99 = 383838383838383838383.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

a(12)=91997 from Ray Chandler, Jul 29 2011
Edited by Ray Chandler, Aug 17 2011

A062231 Numbers k such that the smoothly undulating palindromic number (97*10^k - 79)/99 is a prime.

Original entry on oeis.org

9, 27, 45, 237
Offset: 1

Views

Author

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

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=27 -> (97*10^27 - 79)/99 = 979797979797979797979797979.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Programs

  • Mathematica
    Select[Range[1,239,2],PrimeQ[FromDigits[PadRight[{},#,{9,7}]]]&] (* Harvey P. Dale, Mar 24 2021 *)

Extensions

Edited by Ray Chandler, Aug 17 2011

A062211 Numbers k such that the smoothly undulating palindromic number (15*10^k - 51)/99 is a prime.

Original entry on oeis.org

3, 15, 63, 89, 245, 583, 1791, 2123, 7233, 24787, 44653
Offset: 1

Views

Author

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

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=15 -> (15*10^15 - 51)/99 = 151515151515151.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

a(11)=44653 from Ray Chandler, Nov 11 2010
Edited by Ray Chandler, Aug 17 2011

A062212 Numbers k such that the smoothly undulating palindromic number (16*10^k - 61)/99 is a prime.

Original entry on oeis.org

7, 55, 109, 145, 229, 961
Offset: 1

Views

Author

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

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=7 -> (16*10^7 - 61)/99 = 1616161.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

Edited by Ray Chandler, Aug 17 2011

A062213 Numbers k such that the smoothly undulating palindromic number (17*10^k - 71)/99 is a prime.

Original entry on oeis.org

31, 37, 4885
Offset: 1

Views

Author

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

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=31 -> (17*10^31 - 71)/99 = 1717171717171717171717171717171.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

Edited by Ray Chandler, Aug 17 2011

A062214 Numbers k such that the smoothly undulating palindromic number(18*10^k - 81)/99 is a prime.

Original entry on oeis.org

3, 5, 77, 163, 1479, 3657, 4573, 8315, 30259, 31063, 31855, 36915, 66657
Offset: 1

Views

Author

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

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=5 -> (18*10^5 - 81)/99 = 18181.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

a(13)=66657 from Ray Chandler, Jan 31 2011
Edited by Ray Chandler, Aug 17 2011
Showing 1-10 of 24 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.