A076620 -id:A076620 - cp's OEIS frontend

A341803 a(n) is the least k such that A076620(k) = n.

1, 2, 7, 24, 72, 203, 564, 1556, 4274, 11709, 32021, 87463, 238691

Offset: 0

David A. Corneth, Feb 20 2021

Conjecture: Starting at 7, terms coincide with A309237 - 1. - Hugo Pfoertner, Feb 21 2021

			a(4) = 24 as A076620(24) = 4 while A076620(k) < 4 for k < 24.

Cf. A076620.

With[{s = Array[-1 + FirstPosition[#, Max[#]][[1]] &@ CoefficientList[Pochhammer[x, #]/x, x] &, 600]}, {1}~Join~Array[-1 + FirstPosition[s, #][[1]] &, Max@ s]] (* Michael De Vlieger, Feb 22 2021 *)

first(n) = {res = vector(n); res[1] = 1; my(r = 1); print1(1", "); v = [1]; for(i = 1, oo, v = concat(0, v) + concat(v, 0)*i; if(#v > n, v = v[^-1]; ); for(j = r + 1, #v, if(v[j] > v[j - 1], r++; res[r] = i; print1(i", "); if(r >= n, return(res); ) , next ))); res }

a(n) ~ c*e^n.

A076634 Coefficient of x^a(n) in (x+1/2)(x+2/2)...*(x+n/2) is the largest one.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Benoit Cloitre, Nov 10 2002

nonn

Cf. A076620.

a(n) = my(p=prod(j=1, n, x+j/2), m=vecmax(Vec(p))); for (i=0, poldegree(p), if (polcoef(p, i)==m, return(i))); \\ Michel Marcus, Feb 19 2021

from sympy import prod, Poly
from sympy.abc import x
def A076634(n):
    y = Poly(prod(2*x+i for i in range(1,n+1))).all_coeffs()[::-1]
    return y.index(max(y)) # Chai Wah Wu, Mar 07 2021

A076642 Coefficient of x^a(n) in (x+1/3!)(x+2/3!)...*(x+n/3!) is the largest one.

Original entry on oeis.org

1, 2, 2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15

Offset: 1

Benoit Cloitre, Nov 10 2002

nonn

Cf. A076620, A076634.

a(n) = my(p=prod(j=1, n, x+j/6), m=vecmax(Vec(p))); for (i=0, poldegree(p), if (polcoef(p, i)==m, return(i))); \\ Michel Marcus, Feb 19 2021

from sympy import Poly, rf
from sympy.abc import x
def A076642(n):
    y = Poly(rf(6*x+1,n)).all_coeffs()[::-1]
    return y.index(max(y)) # Chai Wah Wu, Mar 07 2021

cp's OEIS Frontend

A341803 a(n) is the least k such that A076620(k) = n.

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A076634 Coefficient of x^a(n) in (x+1/2)(x+2/2)...*(x+n/2) is the largest one.

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A076642 Coefficient of x^a(n) in (x+1/3!)(x+2/3!)...*(x+n/3!) is the largest one.

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Python

cp's OEIS Frontend

A341803 a(n) is the least k such that A076620(k) = n.

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Author

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Examples

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Mathematica

PARI

Formula

A076634 Coefficient of x^a(n) in (x+1/2)*(x+2/2)*...*(x+n/2) is the largest one.

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Python

A076642 Coefficient of x^a(n) in (x+1/3!)*(x+2/3!)*...*(x+n/3!) is the largest one.

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Author

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PARI

Python

A076634 Coefficient of x^a(n) in (x+1/2)(x+2/2)...*(x+n/2) is the largest one.

A076642 Coefficient of x^a(n) in (x+1/3!)(x+2/3!)...*(x+n/3!) is the largest one.