A056803 -id:A056803 - cp's OEIS frontend

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

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

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

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

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

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

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

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

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

A092696 Smoothly undulating palindromic primes of the form (12*10^n-21)/99.

Original entry on oeis.org

1212121, 12121212121, 1212121212121212121212121212121212121212121

Offset: 1

Rick L. Shepherd, Mar 04 2004

The De Geest link calls these smoothly undulating palindromic primes. Corresponding n are given in A062209. Equivalently, primes of the form 1212...121: Decimal digits "12" repeated k times with 1 appended (or "21" repeated k times with 1 prefixed). Corresponding k are given in A056803. The next term, a(4), has "12" repeating A056803(4) = 69 times and length A062209(4) = 2*A056803(4) + 1 = 139 decimal digits.

Cf. A056803 (number of 12's (or 21's)), A062209 (corresponding decimal digit lengths).

Cf. A032758, A033619, A030291, A059168, A242541, A004022.

a(n) = (4*10^A062209(n)-7)/33. - M. F. Hasler, Jul 30 2015

Edited by M. F. Hasler, Jul 30 2015

A153328 Numbers k such that (10^k-1)*120/99 + 1 is prime.

Original entry on oeis.org

6, 10, 42, 138, 626, 1398, 1596, 1978, 7808, 14058, 46498

Offset: 1

Cino Hilliard, Dec 23 2008

Also 2*A056803 which I took the liberty of using to create the last 2 entries.

These numbers are always even. If n is odd, then 10^n-1 produces a number with an odd number of 9's which 99 does not divide. a(6), a(10), a(42) are 1212121, 12121212121, 1212121212121212121212121212121212121212121 which can be found in A092696. Also, the formula produce palindromic numbers.

Cf. A092696, A056803.

/* n=number of values to test; r=repeat digits, e.g., 12, 121, 177, 1234; d = last digit appended to the end */
repr(n,r,d) = ln=length(Str(r));for(x=0,n,y=(10^(ln*x)-1)*10*r/ (10^ln-1)+1;if(ispseudoprime(y),print1(ln*x",")))

a(11) from Michael S. Branicky, Dec 11 2024

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A092696 Smoothly undulating palindromic primes of the form (12*10^n-21)/99.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A153328 Numbers k such that (10^k-1)*120/99 + 1 is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

Extensions