A122150 -id:A122150

Search: a122150 -id:a122150

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A122151

Indices n such that A122150[n] is a prime.

+20
3

3, 4, 13, 60, 66, 75, 175

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A122150[n] = Numerator[ Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,n} ] ] begins {1,1,5,19,305,1219,19505,78019,1248305,79891519,319566077,20452228927, 327235662833,...}. Primes in A122150[n] are listed in A122152[n] = {5,19,327235662833,...}.

LINKS

Table of n, a(n) for n=1..7.

FORMULA

A122150[ a(n) ] = A122152[n].

MATHEMATICA

Do[f=Numerator[Sum[(-1)^(k+1)*1/2^Prime[k], {k, 1, n}]]; If[PrimeQ[f], Print[{n, f}]], {n, 1, 1000}]

CROSSREFS

Cf. A122150, A122152, A122153.

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Aug 22 2006

STATUS

approved

A122152

Primes in A122150[n] = Numerator[ Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,n} ] ].

+20
3

5, 19, 327235662833, 578175370366880553282134492422436321419543414585625120508329411643068012549226892303, 39731908913255031966162449696446781074231732174358868548789339497630379824042353480418749055951

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A122150[n] = Numerator[ Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,n} ] ] begins {1,1,5,19,305,1219,19505,78019,1248305,79891519,319566077,20452228927,327235662833,...}. Indices of primes in A122150[n] are listed in A122151[n] = {3,4,13,60,66,75,175,...}.

LINKS

Table of n, a(n) for n=1..5.

FORMULA

a(n) = A122150[ A122151[n] ].

MATHEMATICA

Do[f=Numerator[Sum[(-1)^(k+1)*1/2^Prime[k], {k, 1, n}]]; If[PrimeQ[f], Print[{n, f}]], {n, 1, 1000}]

CROSSREFS

Cf. A122150, A122151, A122153.

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Aug 22 2006

STATUS

approved

A122153

Decimal expansion of Parity Prime Constant: Sum_{k>=1} (-1)^(k+1) * 1/(2^prime(k)).

+10
4

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Binary expansion is given in A071986(n) = pi(n) mod 2.

LINKS

Table of n, a(n) for n=0..98.

FORMULA

Equals Sum_{k>=1} (-1)^(k+1) * 1/(2^prime(k)).

Equals lim_{n->infinity} A122150(n)/A034765(n).

EXAMPLE

0.148809550788776224969568467866796531982224132808217067371770000563313912...

MATHEMATICA

RealDigits[Sum[(-1)^(k+1)*1/2^Prime[k], {k, 1, 1000}], 10, 100]

PROG

(PARI) suminf(k=1, (-1)^(k+1) * 1/2^prime(k)) \\ Michel Marcus, Mar 20 2019

CROSSREFS

Cf. A034765, A122150, A122151, A122152, A122153, A071986, A000720.

KEYWORD

nonn,cons

AUTHOR

Alexander Adamchuk, Aug 22 2006

EXTENSIONS

Offset corrected by R. J. Mathar, Feb 05 2009

Edited by Michel Marcus, Mar 20 2019

STATUS

approved

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