|
Search: id:A114992
|
|
|
| A114992 |
|
Primes of the form 2^a * 5^b * 7^c + 1 for positive a, b, c. |
|
+0
1
|
|
| 71, 281, 491, 701, 2801, 4481, 7001, 7841, 12251, 13721, 17921, 28001, 34301, 54881, 70001, 78401, 85751, 122501, 125441, 137201, 168071, 240101, 280001, 286721, 437501, 490001
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Compare with A005109 "Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1." One might call this new sequence "(2,5,7)-Pierpont) primes." This is, since the factors of 2 and 5 are the same as a factor of 10, a subset of A030430 "primes of form 10n+1." There are subsequences such as 71, 701, 7001, 70001, 700001, 700000001, 7000000001; 281, 2801, 280001, 2800001; 491, 490001, 4900001, 490000001, 49000000001, 490000000001.
|
|
FORMULA
|
(For a,b,c>0, 2^a * 5^b * 7^c + 1 IFF prime}. (For a,b,c>0, 2^a * 5^b * 7^c + 1 IFF in A000040}.
|
|
EXAMPLE
|
a(1) = 71 = 2^1 * 5^1 * 7^1 + 1.
a(2) = 281 = 2^3 * 5^1 * 7^1 + 1.
a(3) = 491 = 2^1 * 5^1 * 7^2 + 1.
a(4) = 701 = 2^2 * 5^2 * 7^1 + 1.
a(5) = 2801 = 2^4 * 5^2 * 7^1 + 1.
|
|
CROSSREFS
|
Cf. A000040, A005109, A030430.
Adjacent sequences: A114989 A114990 A114991 this_sequence A114993 A114994 A114995
Sequence in context: A033240 A141943 A140856 this_sequence A126021 A142548 A142143
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 22 2006
|
|
EXTENSIONS
|
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 15 2006
|
|
|
Search completed in 0.002 seconds
|
