A136370
Numerator of 1 - Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.
Original entry on oeis.org
3, 31, 739, 37111, 4446331, 756766039, 217803584371, 78887714418031, 41637516941042299, 35066922176061410359, 33657455280704707522099, 46117280789485930425170431, 77468081652660425646977758411, 143331051198625503752852285686039
Offset: 1
The first few fractions are 3/4, 31/36, 739/900, 37111/44100, 4446331/5336100, 756766039/901800900, ... = A136370/A061742. - _Petros Hadjicostas_, May 14 2020
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Table[Numerator[1 - Sum[(-1)^(k+1)/Prime[k]^2, {k, 1, n}]], {n, 1, 20}]
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a(n) = numerator(1 - sum(k=1, n, (-1)^(k+1)/prime(k)^2)); \\ Michel Marcus, May 14 2020
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from sympy import prime
from fractions import Fraction
from itertools import accumulate, count, islice
def A136370gen(): yield from map(lambda x: (1-x).numerator, accumulate(Fraction((-1)**(k+1), prime(k)**2) for k in count(1)))
print(list(islice(A136370gen(), 14))) # Michael S. Branicky, Jun 26 2022
A136365
Numbers k such that A075986(k) is prime.
Original entry on oeis.org
1, 171, 210, 550, 1445, 1809, 2176, 2719
Offset: 1
Cf.
A075986 (numerator of 1 + 1/p(1)^2 + ... + 1/p(n)^2, where p(k) = prime(k)).
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f=1; Do[ p=Prime[n]; f=f + 1/p^2; g=Numerator[ f ]; If[ PrimeQ[ g ], Print[ {n, g} ] ], {n, 1, 210} ]
A136366
Numbers k such that A024530(k) is prime.
Original entry on oeis.org
3, 4, 5, 10, 21, 31, 55, 77, 121, 135, 148, 192, 425, 570, 612, 649, 1293, 2326, 3646
Offset: 1
Cf.
A024530 (numerator of Sum_{k=1..n} (-1)^k / prime(k)).
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f=0; Do[ p=Prime[n]; f=f + (-1)^(n+1)*1/p; g=Numerator[f] ;If[ PrimeQ[g], Print[ {n, g} ] ], {n, 1, 150} ]
A136368
Numerator of Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.
Original entry on oeis.org
1, 5, 161, 6989, 889769, 145034861, 42816875729, 15196271678069, 8132911703794601, 6790008314246422541, 6567054920481119894801, 8950073675937467308565669, 15100141203716305943432625689
Offset: 1
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[Numerator(&+[(-1)^(k+1)/NthPrime(k)^2:k in [1..n]]): n in [1..13]]; // Marius A. Burtea, Aug 26 2019
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Table[Numerator[Sum[(-1)^(k+1)/Prime[k]^2, {k, 1, n}]], {n, 1, 20}]
A136371
Numbers k such that A136370(k) is prime.
Original entry on oeis.org
1, 2, 3, 5, 46, 227, 232, 336, 360, 3919
Offset: 1
Cf.
A024530: numerator of Sum_{k=1..n} (-1)^k/prime(k).
Cf.
A136368: numerator of Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.
Cf.
A136370: numerator of 1 - Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.
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f=1; Do[ p=Prime[n]; f=f - (-1)^(n+1)*1/p^2; g=Numerator[f] ;If[ PrimeQ[g], Print[ {n, g} ] ], {n, 1, 100} ]
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# uses A136370gen() and imports from A136370
from sympy import isprime
def agen(): yield from (k for k, ak in enumerate(A136370gen(), 1) if isprime(ak))
print(list(islice(agen(), 5))) # Michael S. Branicky, Jun 26 2022
A136367
Numbers k such that A024529(k+1) is prime.
Original entry on oeis.org
2, 3, 4, 5, 11, 59, 397, 613, 906, 1560, 2162, 2915, 5211
Offset: 1
Cf.
A024529: numerator of 1 + Sum_{k=1..n-1} (-1)^k/prime(k).
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f=1; Do[ p=Prime[n]; f=f + (-1)^n*1/p; g=Numerator[f] ;If[ PrimeQ[g], Print[ {n, g} ] ], {n, 1, 60} ]
Showing 1-6 of 6 results.
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