|
| |
|
|
A114835
|
|
Minimal set of palindrome prime-strings in base 10 in the sense of A071062.
|
|
2
|
|
|
|
2, 3, 5, 7, 11, 919, 94049, 94649, 94849, 94949, 96469, 98689, 9809089, 9888889, 9889889, 9908099, 9980899, 9989899, 900808009, 906686609, 906989609, 908000809, 908444809, 908808809, 909848909, 960898069, 968999869, 988000889
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The one-digit primes are palindrome by default so the sequence starts off 2, 3, 5, 7 and so from now on all primes fitting one of the patterns *2*, *3*, *5*, *7* are excluded. The first palindrome prime that is not excluded is 11 so our list is now 2, 3, 5, 7, 11. Observe that from now on all the only palindrome primes allowed have first and last digit 9 and the only middle digits allowed are then 0, 1, 4, 6, 8, 9. But the first and only 3 digit palindrome to occur is 919, so from now on the only middle digits allowed are 0, 4, 6, 8, 9. The five digit palindrome primes that do not fit the patterns *2*, *3*, *5*, *7*, *1*1* and *9*1*9* are 94049, 94649, 94849, 94949, 96469, 98689. The rest of the sequence is determined in this recursive manner.
|
|
|
REFERENCES
|
J.-P. Delahaye, "Pour la science", (French edition of Scientific American), Juin 2002, p. 99.
J. Shallit, Minimal primes, J. Recreational Mathematics, vol. 30.2, pp. 113-117, 1999-2000.
|
|
|
LINKS
|
Walter A. Kehowski, Full list of terms
C. K. Caldwell, The Prime Glossary, minimal prime
J. Shallit, Minimal primes, J. Recreational Mathematics, vol. 30.2, pp. 113-117, 1999-2000.
|
|
|
EXAMPLE
|
a(6)=919 since it is the first 3-digit palindrome prime that does not fit the wildcard pattern established by the previous 5 elements, 2, 3, 5, 7, 11.
|
|
|
MAPLE
|
Maple worksheet available upon request.
|
|
|
CROSSREFS
|
Cf. A071062, A071070.
Sequence in context: A046484 A062888 A046483 * A091689 A046482 A046941
Adjacent sequences: A114832 A114833 A114834 * A114836 A114837 A114838
|
|
|
KEYWORD
|
base,fini,full,nonn
|
|
|
AUTHOR
|
Walter Kehowski, Feb 19 2006
|
|
|
STATUS
|
approved
|
| |
|
|
