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 A083950 Integer coefficients of A(x), where 1<=a(n)<=10, such that A(x)^(1/10) consists entirely of integer coefficients. 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; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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: A241146 A296420 A078267 * A045617 A158486 A280154 Adjacent sequences:  A083947 A083948 A083949 * A083951 A083952 A083953 KEYWORD nonn AUTHOR Paul D. Hanna, May 09 2003 EXTENSIONS More terms from Robert G. Wilson v, Jul 26 2005 STATUS approved

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Last modified October 15 21:06 EDT 2018. Contains 316237 sequences. (Running on oeis4.)