A071087 -id:A071087 - cp's OEIS frontend

A071352 Numbers n such that the sum of two consecutive primes prime(n+1) + prime(n) is a prime power, say q^w. The w values are in A071087.

1, 2, 18, 564, 1462626667154509638735

Offset: 1

Labos Elemer, May 21 2002

			n=1: p(2)+p(1) = 3+2 = 5^1
n=2: p(3)+p(2) = 5+3 = 2^3
n=18: p(19)+p(18) = 61+67 = 2^7
n=564: p(565)+p(564) = 4099+4093 = 2^13

Cf. A071087, A091624.

Do[s=Prime[n+1]+Prime[n]; If[Equal[Length[FactorInteger[s]], 1], Print[{n, Prime[n], s}]], {n, 1, 10000000}]
p = q = 2; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Do[q = NextPrim[p]; If[ Length[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[p + q]]] == 1, Print[n]]; p = q, {n, 1, 10^7}] (* Robert G. Wilson v, Jan 24 2004 *)

For n>1, a(n) = A007053(A071087(n)-1). - Max Alekseyev, Jul 27 2009

a(5) added by Max Alekseyev, Feb 10 2011

A091624 Lesser of consecutive primes whose sum is a perfect power (A001597).

Original entry on oeis.org

3, 17, 47, 61, 71, 107, 283, 881, 1151, 1913, 2591, 3527, 4049, 4093, 6047, 7193, 7433, 10973, 15137, 20807, 21617, 24197, 26903, 28793, 34847, 37039, 46817, 53129, 56443, 69191, 74489, 83231, 84047, 98563, 103049, 103967, 109507, 110441, 112337

Offset: 1

Robert G. Wilson v, Jan 24 2004

nonn

Hans Havermann, Table of n, a(n) for n = 1..10000

Cf. A071087.

Cf. A061275.

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; PrimeExponents[n_] := Flatten[ Table[ #[[2]], {1}] & /@ FactorInteger[n]]; p = q = 2; l = {}; Do[q = NextPrim[p]; If[ Apply[ GCD, PrimeExponents[p + q]] > 1, AppendTo[l, p]]; p = q, {n, 2, 13000}]

A237881 a(n) = 2-adic valuation of prime(n)+prime(n+1).

Original entry on oeis.org

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

Offset: 1

Antonio Roldán, Feb 14 2014

			a(5)=3 because prime(5)=11, prime(6)=13, 11+13=24=2^3*3, 2-adic valuation(24)=3.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A071087, A098048.

IntegerExponent[ListConvolve[{1,1},Prime[Range[200]]],2] (* Paolo Xausa, Nov 02 2023 *)

{for(i=1,200,k=valuation(prime(i)+prime(i+1),2);print1(k,", "))}

from sympy import prime
def A237881(n): return (~(m:=prime(n)+prime(n+1))&m-1).bit_length() # Chai Wah Wu, Jul 08 2022

a(n) = A007814(A001043(n)).

a(n) << log n; in particular, a(n) <= log_2 n + log_2 log n + O(1). - Charles R Greathouse IV, Feb 14 2014

A165744 Numbers k with property that 6^k is the sum of two consecutive primes.

Original entry on oeis.org

2, 3, 7, 36, 54, 143, 1102, 1678

Offset: 1

Zak Seidov, Sep 26 2009

			k=2: 6^2 = 36     = 17 + 19         = prime(7) + prime(8);
k=3: 6^3 = 216    = 107 + 109       = prime(28) + prime(29);
k=7: 6^7 = 279936 = 139967 + 139969 = prime(13005) + prime(13006).

Cf. A071087, A074924.

(* M6 *) Do[If[PreviousPrime[6^n/2]+NextPrime[6^n/2]==6^n,Print[n]],{n,1000}]

is(k) = my(t=6^k); precprime(t/2)+nextprime(1+t/2)==t; \\ Jinyuan Wang, Feb 18 2021

a(7) from Max Alekseyev, Dec 14 2011

a(8) from Amiram Eldar, Apr 06 2019

cp's OEIS Frontend

A071352 Numbers n such that the sum of two consecutive primes prime(n+1) + prime(n) is a prime power, say q^w. The w values are in A071087.

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A091624 Lesser of consecutive primes whose sum is a perfect power (A001597).

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A237881 a(n) = 2-adic valuation of prime(n)+prime(n+1).

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A165744 Numbers k with property that 6^k is the sum of two consecutive primes.

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions