A376051 -id:A376051 - cp's OEIS frontend

A376052 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2k+1)a(k)) < 1.

1, 1, 1, 1, 1, 1, 2, 6, 31, 1527, 3509710, 19634198420529, 670572652324570519822017836, 444183929825540926086588009989665668909119960123355423

Offset: 1

N. J. A. Sloane, Sep 14 2024

nonn

Cf. A374663, A375516, A375531, A375532, A375781, A375522, A376048-A376051, A376053, A376054, A376055.

A376050 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2k-1)a(k)) < 1.

Original entry on oeis.org

2, 1, 2, 3, 6, 172, 137534, 106557767317, 10018727448950607892211, 218107864753736742334588510315735629277159621, 43040465365773907074907163986022284668974202910116417170603263409796800986397420975160781

Offset: 1

N. J. A. Sloane, Sep 13 2024

It appears that S(n) = (e(n)-1)/e(n) for all n != 4, where e(n) = A376051(n). Exceptionally, S(4) = (e(4)-2)/e(4).

a(15) has 1420 decimal digits, too large for a b-file. - Robert Israel, Oct 13 2024

Rémy Sigrist and N. J. A. Sloane, Dampening Down a Divergent Series, Manuscript in preparation, September 2024.

Robert Israel, Table of n, a(n) for n = 1..14

Cf. A374663, A375516, A375531, A375532, A375781, A375522, A376048, A376049, A376051.

S:= 1:R:= NULL:
for i from 1 to 11 do
  r:= ceil(1/((2*i-1)*S));
  if r *(2*i-1) = 1/S then r:= r+1 fi;
  R:= R,r;
  S:= S - 1/((2*i-1)*r)
od:
R; # Robert Israel, Oct 13 2024

A376053 Numerator of the sum S(n) defined in A376052.

Original entry on oeis.org

1, 8, 71, 248, 3043, 43024, 89051, 764441, 451021514, 25508567769, 411827311870583771, 525058386770138717020639964821, 528134692562568161116953143877712480332943632586669596859, 2267693117789905604207315326366543773113615946806750184592188584359364943382168221068055512231683584106110223751

Offset: 1

N. J. A. Sloane, Sep 14 2024

			The initial values of S(n) are 1/3, 8/15, 71/105, 248/315, 3043/3465, 43024/45045, 89051/90090, ...

Cf. A374663, A375516, A375531, A375532, A375781, A375522, A376048-A376051, A376052, A376054, A376055

A376054 Denominator of sum S(n) defined in A376052.

Original entry on oeis.org

3, 15, 105, 315, 3465, 45045, 90090, 765765, 451035585, 25508568085, 411827311870584610, 525058386770138717020639964850, 528134692562568161116953143877712480332943632586669596900

Offset: 1

N. J. A. Sloane, Sep 14 2024

			The initial values of S(n) are 1/3, 8/15, 71/105, 248/315, 3043/3465, 43024/45045, 89051/90090, ...

Cf. A374663, A375516, A375531, A375532, A375781, A375522, A376048-A376051, A376052, A376053, A376055

cp's OEIS Frontend

A376052 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2k+1)a(k)) < 1.

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A376050 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2k-1)a(k)) < 1.

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A376053 Numerator of the sum S(n) defined in A376052.

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A376054 Denominator of sum S(n) defined in A376052.

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cp's OEIS Frontend

A376052 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2*k+1)*a(k)) < 1.

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A376050 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2*k-1)*a(k)) < 1.

Views

Author

Keywords

Comments

References

Links

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Programs

Maple

A376053 Numerator of the sum S(n) defined in A376052.

Views

Author

Keywords

Examples

Crossrefs

A376054 Denominator of sum S(n) defined in A376052.

Views

Author

Keywords

Examples

Crossrefs

A376052 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2k+1)a(k)) < 1.

A376050 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2k-1)a(k)) < 1.