|
Search: id:A094465
|
|
|
| A094465 |
|
Least initial value[=prime=p] for an Euclid/Mullin sequence of which the 4th term equals the n-th prime. p[1]=2 is never a fourth tern, so offset=2. |
|
+0
1
|
|
| 5, 19, 43, 31, 67, 541, 193, 157, 1213, 811, 487, 2371, 2, 1543, 733, 1319, 1291, 1753, 1621, 2713, 13, 1231, 2833, 2053, 1801, 3313, 5011, 821, 2467, 5101, 3253, 8573, 3637, 1553, 15427, 5521, 3191, 9173, 7237, 10531, 11071, 6271, 9103, 15727, 7993
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
FORMULA
|
a[n]=Min[x; A051614(x)=p(n)=A000040(n)]
|
|
EXAMPLE
|
n=14:p[14]=43 and an Euclid-Mullin sequence started
with a[14]=2=p(1) is {2,3,7,43,13,53,5,6221671,38709183810571,139,..} is
A000945, the prototype EM-sequence.
n=7:a[7]=541, the 100th prime, with EM sequence as follows:
{541,2,3,17,139,7,1871,100457892907,19,11047..}, where the 4th
term equals p[n]=p[7]=17.
It is characteristic but not so simple congruence
relations holds of Mod[term[1],term[4]] form for
various first or 4rd primes, not necessarily smallest ones.
See comment to A094464.
|
|
MATHEMATICA
|
a[x_]:=First[Flatten[FactorInteger[Apply[Times, Table[a[j], {j, 1, x-1}]]+1]]]; ta=Table[0, {20000}]; a[1]=1; Do[{a[1]=Prime[j], el=4}; ta[[j]]=a[el], {j, 1, 20000}] Table[Prime[Min[Flatten[Position[ta, Prime[w]]]]], {w, 1, 100}]
|
|
CROSSREFS
|
Cf. A000945, A051308-A051334, A094460, A094464.
Sequence in context: A089148 A098319 A022267 this_sequence A020580 A045458 A120289
Adjacent sequences: A094462 A094463 A094464 this_sequence A094466 A094467 A094468
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu), May 10 2004
|
|
|
Search completed in 0.002 seconds
|
