|
Search: id:A107125
|
|
|
| A107125 |
|
Numbers n such that (10^(2n+1)+36*10^n-1)/9 is prime. |
|
+0
2
|
|
| 0, 1, 7, 45, 115, 681, 1248, 2481, 2689, 6198, 13197
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
n is in the sequence iff the palindromic number 1(n).5.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+2, 18m+12, 18m+14, 22m+4, 22m+6, etc. (the proof is easy).
|
|
REFERENCES
|
C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
|
|
LINKS
|
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Factorizations of 11...11511...11
|
|
FORMULA
|
a(n) = (A077783(n)-1)/2.
|
|
EXAMPLE
|
1248 is in the sequence because (10^(2*1248+1)+36*10^1248-1)/9=1(1248).5.1(1248) is prime.
|
|
MATHEMATICA
|
Do[If[PrimeQ[(10^(2n + 1) + 36*10^n - 1)/9], Print[n]], {n, 2200}]
|
|
CROSSREFS
|
Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A114633-A114647.
Sequence in context: A156374 A171493 A153492 this_sequence A059937 A099842 A115194
Adjacent sequences: A107122 A107123 A107124 this_sequence A107126 A107127 A107128
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Farideh Firoozbakht (mymontain(AT)yahoo.com), May 19 2005
|
|
|
Search completed in 0.002 seconds
|
