A086242 -id:A086242 - cp's OEIS frontend

A382581 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*(p + 1)^3).

0, 4, 1, 2, 9, 6, 5, 3, 7, 8, 8, 3, 1, 3, 7, 1, 3, 6, 7, 7, 4, 5, 9, 4, 2, 4, 9, 8, 6, 9, 9, 1, 1, 6, 9, 3, 6, 8, 7, 5, 6, 2, 4, 5, 2, 4, 9, 2, 5, 4, 2, 3, 4, 8, 1, 4, 5, 4, 2, 0, 0, 4, 6, 4, 1, 1, 3, 0, 0, 7, 8, 3, 5, 5, 8, 3, 5, 7, 2, 8, 0, 8, 1, 4, 5, 2, 1, 8, 2, 9, 1, 3, 0, 9, 8, 9, 3, 9, 9, 1, 4

Offset: 0

Artur Jasinski, Mar 31 2025

			0.0412965378831371367745942498699116936875624524925423481454200464113007835583572808145218...

Index to constants which are prime zeta sums {0,2,3}.

Cf. A086242, A136141, A179119, A382554, A382555.

sumeulerrat(1/((p-1)^2*(p+1)^3)) \\ Amiram Eldar, Apr 02 2025

Equals -3*A136141/16 + A086242/8 - 3*A179119/16 + A382554/4 + A382555/4.

Equals Sum_{k>=3} ((k-2)*(k-1)/2) * (P(2*k-1) - P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025

A382585 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^2(p + 1)).

Original entry on oeis.org

0, 9, 0, 7, 7, 6, 5, 9, 9, 5, 3, 7, 0, 8, 8, 4, 2, 2, 3, 8, 0, 9, 3, 6, 9, 5, 8, 2, 5, 1, 8, 5, 3, 5, 9, 9, 0, 7, 8, 5, 3, 9, 7, 9, 8, 3, 5, 5, 0, 5, 0, 9, 7, 6, 6, 6, 4, 6, 9, 8, 8, 6, 3, 9, 1, 0, 2, 9, 1, 0, 5, 6, 6, 2, 4, 9, 1, 9, 7, 6, 8, 7, 9, 1, 2, 3, 7, 1, 2, 0, 1, 5, 5, 7, 4, 1, 1, 1, 6, 7, 9, 5, 1, 4, 2

Offset: 0

Artur Jasinski, Mar 31 2025

			0.09077659953708842238093695825185359907853979835505...

Index to constants which are prime zeta sums {2,2,1}.

Cf. A085548, A086242, A136141, A179119.

sumeulerrat(1/((p-1)^2*p^2*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals A085548 - 5*A136141/4 + A086242/2 - A179119/4.

Equals Sum_{k>=3} (k-2) * (P(2*k-1) + P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382586 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^3(p + 1)).

Original entry on oeis.org

0, 4, 4, 0, 7, 5, 8, 6, 7, 4, 4, 3, 7, 3, 6, 0, 1, 5, 3, 7, 9, 4, 1, 3, 8, 3, 7, 0, 3, 2, 9, 6, 1, 4, 8, 2, 5, 6, 6, 7, 1, 0, 9, 6, 1, 9, 7, 6, 6, 4, 2, 4, 7, 0, 4, 7, 2, 9, 8, 2, 1, 4, 7, 3, 1, 4, 7, 7, 9, 2, 1, 5, 3, 0, 4, 8, 8, 6, 6, 2, 9, 6, 7, 0, 8, 2, 3, 5, 4, 5, 0, 3, 7, 6, 7, 0, 8, 1, 9, 7, 3, 8, 0, 5, 4

Offset: 0

Artur Jasinski, Mar 31 2025

			0.044075867443736015379413837032961482566710961976642...

Index to constants which are prime zeta sums {3,2,1}.

Cf. A085541, A085548, A086242, A136141, A179119.

sumeulerrat(1/((p-1)^2*p^3*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals A085548 + A085541 - 7*A136141/4 + A086242/2 + A179119/4.

Equals Sum_{k>=3} (k-2) * (P(2*k) + P(2*k+1)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382587 Decimal expansion of Sum_{p prime} 1/((p - 1)^3p(p + 1)) .

Original entry on oeis.org

1, 7, 7, 6, 9, 9, 1, 4, 7, 4, 5, 3, 3, 5, 8, 8, 8, 9, 2, 8, 3, 1, 3, 6, 7, 5, 9, 1, 1, 2, 3, 4, 1, 9, 2, 7, 5, 2, 3, 5, 4, 8, 6, 3, 9, 2, 6, 9, 5, 9, 7, 0, 1, 8, 8, 5, 9, 3, 7, 1, 7, 9, 3, 8, 9, 8, 6, 5, 7, 6, 3, 9, 4, 5, 0, 3, 2, 2, 0, 0, 4, 2, 2, 8, 2, 5, 6, 4, 1, 7, 4, 0, 5, 1, 5, 5, 7, 1, 5, 6, 2, 7, 8, 0, 8

Offset: 0

Artur Jasinski, Mar 31 2025

			0.17769914745335888928313675911234192752354863926959...

Index to constants which are prime zeta sums {1,3,1}.

Cf. A086242, A136141, A179119, A380840.

sumeulerrat(1/((p-1)^3*p*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals 7*A136141/8 - 3*A086242/4 + A380840/2 - A179119/8.

Equals Sum_{k>=3} ((k-2)^2 * P(2*k-1) + (k-2)*(k-1) * P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382588 Decimal expansion of Sum_{p prime} 1/((p - 1)^3p^2(p + 1)).

Original entry on oeis.org

0, 8, 6, 9, 2, 2, 5, 4, 7, 9, 1, 6, 2, 7, 0, 4, 6, 6, 9, 0, 2, 1, 9, 9, 8, 0, 0, 8, 6, 0, 4, 8, 8, 3, 2, 8, 4, 4, 5, 0, 0, 8, 8, 4, 0, 9, 1, 4, 5, 4, 6, 0, 4, 2, 1, 9, 4, 6, 7, 2, 9, 2, 9, 9, 8, 8, 3, 6, 6, 5, 8, 2, 8, 2, 5, 4, 0, 2, 2, 3, 5, 4, 3, 7, 0, 1, 9, 2, 9, 7, 2, 4, 9, 4, 1, 4, 5, 9, 8, 8, 3, 2, 6, 6

Offset: 0

Artur Jasinski, Mar 31 2025

			0.08692254791627046690219980086048832844500884091454...

Index to constants which are prime zeta sums {2,3,1}.

Cf. A085548, A086242, A136141, A179119, A380840.

sumeulerrat(1/((p-1)^3*p^2*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals -A085548 + 17*A136141/8 - 5*A086242/4 + A380840/2 + A179119/8.

Equals Sum_{k>=3} ((k-2)^2 * P(2*k) + (k-2)*(k-1) * P(2*k+1)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382589 Decimal expansion of Sum_{p prime} 1/((p - 1)^3p^3(p + 1)).

Original entry on oeis.org

0, 4, 2, 8, 4, 6, 6, 8, 0, 4, 7, 2, 5, 3, 4, 4, 5, 1, 5, 2, 2, 7, 8, 5, 9, 6, 3, 8, 2, 7, 5, 2, 6, 8, 4, 5, 8, 7, 8, 2, 9, 7, 8, 7, 8, 9, 3, 7, 9, 0, 3, 5, 7, 1, 7, 2, 1, 6, 9, 0, 7, 8, 2, 6, 7, 3, 5, 8, 7, 3, 6, 7, 5, 2, 0, 5, 1, 5, 6, 0, 5, 7, 6, 6, 1, 9, 5, 7, 5, 2, 2, 1, 1, 7, 4, 3, 7, 7, 9, 0, 9, 4, 6, 1

Offset: 0

Artur Jasinski, Mar 31 2025

			0.04284668047253445152278596382752684587829787893790...

Index to constants which are prime zeta sums {3,3,1}.

Cf. A085541, A085548, A086242, A136141, A179119, A380840.

sumeulerrat(1/((p-1)^3*p^3*(p+1))) \\ Amiram Eldar, Apr 01 2025

Equals -2*A085548 - A085541 + 31*A136141/8 - 7*A086242/4 + A380840/2 - A179119/8.

Equals Sum_{k>=4} ((k-3)^2 * P(2*k-1) + (k-3)*(k-2) * P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382594 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p(p + 1)^2).

Original entry on oeis.org

0, 6, 1, 1, 8, 3, 5, 5, 1, 2, 5, 5, 2, 1, 4, 5, 5, 1, 8, 1, 6, 6, 8, 9, 7, 5, 3, 9, 0, 9, 1, 7, 3, 3, 6, 5, 3, 9, 8, 3, 1, 5, 6, 1, 8, 6, 9, 4, 5, 8, 1, 1, 1, 8, 8, 5, 8, 4, 8, 4, 5, 6, 3, 0, 5, 4, 7, 1, 0, 9, 6, 1, 1, 7, 1, 1, 6, 2, 5, 2, 5, 5, 2, 0, 0, 5, 8, 8, 8, 1, 1, 3, 3, 1, 3, 0, 2, 8, 4, 9, 1, 7, 2, 1, 5

Offset: 0

Artur Jasinski, Mar 31 2025

			0.06118355125521455181668975390917336539831561869458...

Index to constants which are prime zeta sums {1,2,2}.

Cf. A086242, A136141, A179119, A382554.

sumeulerrat(1/((p-1)^2*p*(p+1)^2)) \\ Amiram Eldar, Apr 01 2025

Equals -A136141/2 + A086242/4 + A179119/2 - A382554/4.

Equals Sum_{k>=3} (k-2) * P(2*k-1), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382595 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^2(p + 1)^2).

Original entry on oeis.org

0, 2, 9, 5, 9, 3, 0, 4, 8, 2, 8, 1, 8, 7, 3, 8, 7, 0, 5, 6, 4, 2, 4, 7, 2, 0, 4, 3, 4, 2, 6, 8, 0, 2, 3, 3, 6, 8, 0, 2, 2, 4, 1, 7, 9, 6, 6, 0, 4, 6, 9, 8, 5, 7, 8, 0, 6, 2, 1, 4, 3, 0, 0, 8, 5, 5, 5, 8, 0, 0, 9, 5, 4, 5, 3, 7, 5, 7, 2, 4, 3, 2, 7, 1, 1, 7, 8, 2, 3, 9, 0, 2, 2, 6, 1, 0, 8, 3, 1, 8, 7, 7, 9

Offset: 0

Artur Jasinski, Mar 31 2025

			0.02959304828187387056424720434268023368022417966046...

Index to constants which are prime zeta sums {2,2,2}.

Cf. A085548, A086242, A136141, A179119, A382554.

sumeulerrat(1/((p-1)^2*p^2*(p+1)^2)) \\ Amiram Eldar, Apr 01 2025

Equals A085548 - 3*A136141/4 + A086242/4 - 3*A179119/4 + A382554/4.

Equals Sum_{k>=3} (k-2) * P(2*k), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382596 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^3(p + 1)^2).

Original entry on oeis.org

0, 1, 4, 4, 8, 2, 8, 1, 9, 1, 6, 1, 8, 6, 2, 1, 4, 4, 8, 1, 5, 1, 6, 6, 6, 3, 2, 6, 9, 0, 2, 8, 1, 2, 4, 8, 8, 8, 6, 4, 8, 6, 7, 8, 2, 3, 1, 6, 1, 7, 2, 6, 1, 2, 6, 6, 6, 7, 6, 7, 8, 4, 6, 4, 5, 9, 1, 9, 9, 1, 1, 9, 8, 5, 1, 1, 2, 9, 3, 8, 6, 3, 9, 9, 6, 4, 5, 3, 0, 6, 0, 1, 5, 0, 5, 9, 9, 8, 7, 8, 6, 0, 1, 2

Offset: 0

Artur Jasinski, Mar 31 2025

			0.01448281916186214481516663269028124888648678231617...

Index to constants which are prime zeta sums {3,2,2}.

Cf. A085541, A086242, A136141, A179119, A382554.

sumeulerrat(1/((p-1)^2*p^3*(p+1)^2)) \\ Amiram Eldar, Apr 01 2025

Equals A085541 - A136141 + A086242/4 + A179119 - A382554/4.

Equals Sum_{k>=3} (k-2) * P(2*k+1), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

A382598 Decimal expansion of Sum_{p prime} 1/((p - 1)^3p(p + 1)^2).

Original entry on oeis.org

0, 5, 8, 2, 5, 7, 7, 9, 8, 0, 9, 9, 0, 7, 2, 1, 6, 8, 7, 3, 3, 2, 2, 3, 5, 0, 2, 6, 0, 1, 5, 8, 4, 2, 8, 1, 0, 6, 2, 6, 1, 6, 5, 1, 0, 2, 8, 7, 5, 0, 7, 9, 5, 0, 0, 0, 0, 4, 4, 3, 6, 1, 5, 4, 2, 1, 9, 7, 3, 3, 3, 9, 1, 3, 9, 5, 7, 9, 7, 3, 9, 3, 5, 4, 0, 9, 8, 7, 6, 8, 1, 3, 6, 0, 1, 2, 7, 1, 5, 3, 5, 5, 2

Offset: 0

Artur Jasinski, Mar 31 2025

			0.05825779809907216873322350260158428106261651028750...

Index to constants which are prime zeta sums {1,3,2}.

Cf. A086242, A136141, A179119, A380840, A382554.

sumeulerrat(1/((p-1)^3*p*(p+1)^2)) \\ Amiram Eldar, Apr 01 2025

Equals 11*A136141/16 - A086242/2 + A380840/4 - 5*A179119/16 + A382554/8.

Equals Sum_{k>=3} ((k-2)*(k-1)/2)*(P(2*k) + P(2*k+1)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

cp's OEIS Frontend

A382581 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*(p + 1)^3).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A382585 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*p^2*(p + 1)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A382586 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*p^3*(p + 1)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A382587 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*p*(p + 1)) .

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A382588 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*p^2*(p + 1)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A382589 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*p^3*(p + 1)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A382594 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*p*(p + 1)^2).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A382595 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*p^2*(p + 1)^2).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

A382585 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^2(p + 1)).

A382586 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^3(p + 1)).

A382587 Decimal expansion of Sum_{p prime} 1/((p - 1)^3p(p + 1)) .

A382588 Decimal expansion of Sum_{p prime} 1/((p - 1)^3p^2(p + 1)).

A382589 Decimal expansion of Sum_{p prime} 1/((p - 1)^3p^3(p + 1)).

A382594 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p(p + 1)^2).

A382595 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^2(p + 1)^2).

A382596 Decimal expansion of Sum_{p prime} 1/((p - 1)^2p^3(p + 1)^2).

A382598 Decimal expansion of Sum_{p prime} 1/((p - 1)^3p(p + 1)^2).