A132822 -id:A132822 - cp's OEIS frontend

A132817 Decimal expansion of Sum_{n >= 1} 1/6^prime(n).

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

Offset: 0

Cino Hilliard, Nov 17 2007

Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-6 expansion. - M. F. Hasler, Jul 05 2017

			0.032539583308525544049260050781274181192986076617578098887664610099...

Vincenzo Librandi, Table of n, a(n) for n = 0..1110

Cf. A000720, A051006 (analog for base 2), A132800 (analog for base 3), A132806 (analog for base 4), A132797 (analog for base 5), A132822 (analog for base 7), A010051 (characteristic function of the primes), A000040 (the primes).

Join[{0}, RealDigits[FromDigits[{{Table[If[PrimeQ[n], 1, 0], {n, 370}]}, 0}, 6], 10, 111][[1]]] (* Vincenzo Librandi, Jul 05 2017 *)

/* Sum of 1/m^p for primes p */ sumnp(n,m) = { local(s=0,a,j); for(x=1,n, s+=1./m^prime(x); ); a=Vec(Str(s)); for(j=3,n, print1(eval(a[j])",") ) }

suminf(n=1, 1/6^prime(n)) \\ Then: digits(%\.1^default(realprecision))[1..-3] to remove the last 2 digits. N.B.: Functions sumpos() and sumnum() yield much less accurate results. - M. F. Hasler, Jul 04 2017

Equals 5 * Sum_{k>=1} pi(k)/6^(k+1), where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020

Offset corrected R. J. Mathar, Jan 26 2009

Edited by M. F. Hasler, Jul 05 2017

A132799 Decimal expansion of the convergent to the sum of (1/8)^p where p ranges over the set of prime numbers.

Original entry on oeis.org

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

Offset: 0

Cino Hilliard, Nov 17 2007

			0.01760911...

Cf. A000720, A132822 (base 7), A132821 (base 9).

/* Sum of 1/m^p for primes p */ sumnp(n,m) = { local(s=0,a,j); for(x=1,n, s+=1./m^prime(x); ); a=Vec(Str(s)); for(j=3,n, print1(eval(a[j])",") ) }

Equals 7 * Sum_{k>=1} pi(k)/8^(k+1), where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020

Offset corrected R. J. Mathar, Jan 26 2009

A269327 a(n) = 7^prime(n).

Original entry on oeis.org

49, 343, 16807, 823543, 1977326743, 96889010407, 232630513987207, 11398895185373143, 27368747340080916343, 3219905755813179726837607, 157775382034845806615042743, 18562115921017574302453163671207, 44567640326363195900190045974568007

Offset: 1

Emre APARI, Feb 23 2016

			The second prime is 3, hence a(2) = 7^3 = 343.
The third prime is 5, hence a(3) = 7^5 = 16807.

Cf. A000040, A000420, A034785, A053810, A057901, A057902, A132822.

[7^p: p in PrimesUpTo(45)]; // Vincenzo Librandi, Feb 25 2016

A269327:=n->7^ithprime(n): seq(A269327(n), n=1..20); # Wesley Ivan Hurt, Mar 07 2016

7^Prime[Range[20]] (* Alonso del Arte, Feb 23 2016 *)

a(n) = 7^prime(n); \\ Altug Alkan, Mar 04 2016

a(n) = 7^A000040(n).

Sum_{n>=1} 1/a(n) = A132822. - Amiram Eldar, Aug 11 2020

cp's OEIS Frontend

A132817 Decimal expansion of Sum_{n >= 1} 1/6^prime(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A132799 Decimal expansion of the convergent to the sum of (1/8)^p where p ranges over the set of prime numbers.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula

Extensions

A269327 a(n) = 7^prime(n).

Views

Author

Keywords

Examples

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula