|
Search: id:A065840
|
|
|
| A065840 |
|
Numbers n such that the first n quaternary digits found in the base-10 expansion of pi form a prime (when the decimal point is ignored). |
|
+0
13
|
|
| 1, 2, 3, 5, 10, 19, 72, 115, 220, 315, 375
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
In other words, take the decimal expansion of pi, drop any digits greater than 4, omit the decimal point and look for prefixes in the resulting string which form base-4 primes.
Numbers n such that A065838(n) is prime.
|
|
EXAMPLE
|
E.g. the first a(5) or 10 quaternary digits of pi are 31.12332323{4} and 3112332323{4} is the prime 880571{10}.
|
|
MATHEMATICA
|
p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 || p[[ # ]] == 2 || p[[ # ]] == 3 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 4]], Print[ n]], {n, 1, 4000} ]
|
|
CROSSREFS
|
Cf. A065828 up to A065839, A000796, A011545, A011546, A055145, A005042, A060421, A039954, A048796.
Sequence in context: A064236 A007569 A054317 this_sequence A093785 A105369 A047101
Adjacent sequences: A065837 A065838 A065839 this_sequence A065841 A065842 A065843
|
|
KEYWORD
|
nonn,base,hard
|
|
AUTHOR
|
Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 24 2001.
|
|
|
Search completed in 0.002 seconds
|
