|
Search: id:A113914
|
|
|
| A113914 |
|
(1,2,3) Jasinski-like positive power sequence. |
|
+0
2
|
|
| 1, 5, 13, 29, 61, 131, 271, 569, 1381, 2789, 5581, 11171, 22369, 44741, 89491, 185543, 373273, 766229, 1532701, 3065411, 6130849, 12261701, 24700549, 49401101, 98802211, 202387391, 409557751, 819116231, 1638232471, 3276464969
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
In general, the (b,c,d) Jasinski-like positive power sequence is defined as follows: a(1) = b, a(n+1) = the least prime p such that p = c*a(n) + d^k for positive integer k. The (b,c,d) Jasinski-like nonnegative power sequence is defined: a(1) = b, a(n+1) = the least prime p such that p = c*a(n) + d^k for integer k. In this notation, A113824 is the (1,2,2) Jasinski-like nonnegative power sequence. The first differences of such sequences are powers of d, with no closed-form known upper bound.
|
|
FORMULA
|
a(1) = 1, a(n+1) = the least prime p such that p = 2*a(n) + 3^k for integer k>0.
|
|
EXAMPLE
|
a(1) = 1 by definition.
a(2) = 2*1 + 3^1 = 5.
a(3) = 2*5 + 3^1 = 13.
a(4) = 2*13 + 3^1 = 29.
a(5) = 2*29 + 3^1 = 61.
a(6) = 2*61 + 3^2 = 271.
a(7) = 2*271 + 3^2 = 569.
a(32) = 2*6553461379 + 3^49 = 239299329230630636512841. Here 49 is a record value for the exponent.
|
|
CROSSREFS
|
Cf. A073924, A080355, A080567, A099969, A099970, A099971, A099972, A113824.
Sequence in context: A120274 A036982 A029580 this_sequence A050415 A099970 A073857
Adjacent sequences: A113911 A113912 A113913 this_sequence A113915 A113916 A113917
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 29 2006
|
|
|
Search completed in 0.002 seconds
|
