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 A083948 Integer coefficients of A(x), where 1<=a(n)<=8, such that A(x)^(1/8) consists entirely of integer coefficients. 15
 1, 8, 4, 8, 2, 8, 4, 8, 7, 8, 8, 8, 4, 8, 8, 8, 3, 8, 8, 8, 2, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 6, 8, 4, 8, 6, 8, 4, 8, 6, 8, 8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 6, 8, 8, 8, 8, 8, 4, 8, 6, 8, 4, 8, 8, 8, 8, 8, 6, 8, 8, 8, 7, 8, 4, 8, 8, 8, 4, 8, 3, 8, 4, 8, 4, 8, 4, 8, 3 (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)^(1/8), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *) CROSSREFS Cf. A083952, A083953, A083954, A083955, A083956, A083947, A083949, A083950. Sequence in context: A199266 A347145 A205383 * A021848 A021545 A141614 Adjacent sequences:  A083945 A083946 A083947 * A083949 A083950 A083951 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 January 28 20:33 EST 2022. Contains 350662 sequences. (Running on oeis4.)