A089592 For any prime p, define a sequence S_p: S_p(1) = p and S_p(n+1) is the least prime > S_p(n) that begins with the last digit of S_p(n). Let f(p) be the first member of S_p that is the digit reversal of the previous member. Sequence contains primes p that such that f(p) does not equal f(q) for any q < p.

2, 11, 17, 79, 107, 109, 709, 4003, 10009, 11003, 1000039, 1100009, 400000043, 1000000009, 150000000000007

Offset

1,1

Comments

The corresponding values f(a(n)) are 9001, 31, 71, 97, 701, 70001, 907, 7*10^8+1, 90001, 30011, 7*10^9+1, 9000011, 9*10^22+1, 9*10^9+1, 7*10^14+51, 7*10^19+13, 9*10^46+7, 7*10^50+43, 9*10^60+227. p = 4*10^45-47 (between a(18) and a(19)) appears to be the first prime such that f(p) doesn't exist: the digit reversal doesn't occur < 10^300 and is unlikely to occur later. - David Wasserman, Oct 03 2005

Links

Table of n, a(n) for n=1..15.

Formula

Begin with any prime, continue with the next prime having same beginning digit as that of the last digit of the prime preceding until the first prime reversal is found.

Example

In the sequence beginning with the prime 2, continue 23 31 101 103 307 701 1009 9001 . . . . [A061448]. The first occurrence of a prime reversal beginning with the prime 2 is 1009 and 9001. This is a different first occurrence prime reversal than that found in the sequence beginning with 11 which continues to 13 31.

Crossrefs

Cf. A061448.

Sequence in context: A217306 A106981 A176985 * A106982 A347600 A043461

Adjacent sequences: A089589 A089590 A089591 * A089593 A089594 A089595

Keyword

nonn,base,less

Author

Enoch Haga, Dec 29 2003

Extensions

More terms from David Wasserman, Oct 03 2005

Incorrect terms removed by Charles R Greathouse IV, Nov 21 2014

Status

approved