|
Search: id:A083950
|
|
|
| A083950 |
|
Integer coefficients of A(x), where 1<=a(n)<=10, such that A(x)^(1/10) consists entirely of integer coefficients. |
|
+0
13
|
|
| 1, 10, 5, 10, 10, 2, 5, 10, 10, 10, 3, 10, 5, 10, 10, 2, 10, 10, 10, 10, 5, 10, 5, 10, 5, 8, 5, 10, 5, 10, 8, 10, 10, 10, 10, 4, 5, 10, 10, 10, 7, 10, 10, 10, 5, 2, 10, 10, 5, 10, 7, 10, 5, 10, 5, 4, 10, 10, 10, 10, 7, 10, 10, 10, 10, 2, 5, 10, 5, 10, 9, 10, 5, 10, 5, 6, 5, 10, 10, 10, 8
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
More generally, the sequence, "integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m. Are these sequences periodic?
|
|
LINKS
|
Robert G. Wilson v, Table of n, a(n) for n = 0..3000.
|
|
MATHEMATICA
|
a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/10), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 80}] (* Robert G. Wilson v *)
|
|
CROSSREFS
|
Cf. A083952, A083953, A083954, A083952, A083956, A083947, A083948, A083949.
Sequence in context: A147653 A152611 A078267 this_sequence A045617 A158486 A040093
Adjacent sequences: A083947 A083948 A083949 this_sequence A083951 A083952 A083953
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), May 09 2003
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jul 26 2005
|
|
|
Search completed in 0.002 seconds
|
