A104907 -id:A104907 - cp's OEIS frontend

A105322 Primes of the form 8*10^n-7.

73, 7993, 799993, 7999993, 79999999993, 7999999999993, 79999999999993, 7999999999999999999999999999999999999993, 7999999999999999999999999999999999999999999999993

Offset: 1

Farideh Firoozbakht, Apr 16 2005

This sequence is a subsequence of A104907 also is a subsequence of A105324(see A104907 and A105324).

			7993 is in the sequence because 7993=8*10^3-7 and 7993 is prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..16
Makoto Kamada, Prime numbers of the form 799...993.

Cf. A099190, A104907, A105324.

[ a: n in [0..50] | IsPrime(a) where a is 8*10^n-7 ]; // Vincenzo Librandi, Jul 19 2012

Do[If[PrimeQ[8*10^n - 7], Print[8*10^n - 7]], {n, 60}]
Select[Table[8*10^n-7,{n,0,80}],PrimeQ] (* Vincenzo Librandi, Jul 19 2012 *)

a(n) = 8*A099190(n) - 7.

A105323 Numbers of the form 41(210^n+1) where (2*10^n+1)/3 is prime (n is in the sequence A096507).

Original entry on oeis.org

861, 8241, 82000041, 8200000041, 82000000041, 8200000000041, 8200000000000000000041, 8200000000000000000000041, 8200000000000000000000000000000000000000041

Offset: 1

Farideh Firoozbakht, Apr 16 2005

nonn

A105323=41*A093170=41*(2*10^A096507+1)=41*(2*10^(A056657+1)+1). If m is in the sequence then d(m)*reversal(m)=sigma(m) (see A104907). So this sequence is a subsequence of A104907.

			861 is in the sequence because 861=41*(2*10^1+1); (2*10^1+1)/3=7 and 7 is prime.

Cf. A104907, A056657, A096507, A093170.

Do[If[PrimeQ[(2*10^n + 1)/3], Print[41*(2*10^n + 1)]], {n, 63}]

A104906 Numbers n such that d(n)*reversal(n)=phi(n), where d(n) is number of positive divisors of n.

Original entry on oeis.org

1, 10, 831, 8310

Offset: 1

Farideh Firoozbakht, Apr 14 2005

If n is a term of this sequence and gcd(10,n)=1 then 10*n is also in the sequence because reversal(10*n)=reversal(n); d(10)=phi(10) and both functions d & phi are multiplicative. No further terms up to 350000000.

a(5) > 10^12. - Giovanni Resta, Apr 25 2017

			8310 is in the sequence because d(8310)=16; reversal(8310)=138;
phi(8310)=2208 & 16*138=2108.

Cf. A063903, A104904, A104905, A104907.

reversal[n_]:= FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[0, n]*reversal[n] == EulerPhi[n], Print[n]], {n, 350000000}]

cp's OEIS Frontend

A105322 Primes of the form 8*10^n-7.

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A105323 Numbers of the form 41(210^n+1) where (2*10^n+1)/3 is prime (n is in the sequence A096507).

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A104906 Numbers n such that d(n)*reversal(n)=phi(n), where d(n) is number of positive divisors of n.

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cp's OEIS Frontend

A105322 Primes of the form 8*10^n-7.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A105323 Numbers of the form 41*(2*10^n+1) where (2*10^n+1)/3 is prime (n is in the sequence A096507).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A104906 Numbers n such that d(n)*reversal(n)=phi(n), where d(n) is number of positive divisors of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A105323 Numbers of the form 41(210^n+1) where (2*10^n+1)/3 is prime (n is in the sequence A096507).