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A112283 Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This sequence is the first occurrence of 1 after the first column. 3
1, 2, 3, 8, 5, 72, 7, 24, 9, 130, 11, 264, 13, 168, 210, 304, 17, 162, 19, 540, 378, 682, 23, 456, 25, 1274, 27, 336, 29, 1770, 31, 544, 2013, 918, 525, 504, 37, 3724, 234, 280, 41, 504, 43, 4180, 2025, 414, 47, 816, 49, 1300, 3723, 1196, 53, 972, 550, 1960, 3933, 986, 59, 6480, 61, 1798, 4095, 1792, 3055 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The degree >0 of the polynomial above whose coefficient is 1.

LINKS

Table of n, a(n) for n=1..65.

FORMULA

Conjecture: a(n)=n if n is 1, a prime or the square of the odd primes.

EXAMPLE

Only the pertinent part of the 'Table' in A109626.

{1, 1},

{1, 2, 1},

{1, 3, 3, 1},

{1, 4, 2, 4, 3, 4, 4, 4, 1},

{1, 5, 5, 5, 5, 1},

{1, 6, 3, 2, 3, 6, 6, 6, 3, 4, 6, 6, 6, 6, ..., },

{1, 7, 7, 7, 7, 7, 7, 1},

{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},

{1, 9, 9, 3, 9, 9, 3, 9, 9, 1},

{1, 10, 5, 10, 10, 2, 5, 10, 10, 10, 3, 10, 5, 10, ..., },

{1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1},

{1, 12, 6, 4, 9, 12, 4, 12, 12, 8, 6, 12, 6, 12, ..., },

{1, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 1}, ...,.

MATHEMATICA

f[n_] := Module[{j = 1, a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; While[a[j] != 1, j++ ]; j]; Table[ f[n], {n, 10}]

CROSSREFS

Cf. A109626, A112284.

Sequence in context: A162537 A109844 A128779 * A136182 A170911 A067911

Adjacent sequences:  A112280 A112281 A112282 * A112284 A112285 A112286

KEYWORD

nonn

AUTHOR

Paul D. Hanna and Robert G. Wilson v, Aug 20 2005

EXTENSIONS

a(30)-a(50) from Robert G. Wilson v, Oct 29 2007

a(51)-a(65) from Robert G. Wilson v, Jul 25 2008

STATUS

approved

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Last modified December 11 11:31 EST 2017. Contains 295876 sequences.