A039655 -id:A039655 - cp's OEIS frontend

A292113 List of numbers n such that A039654(n) reaches a new record high.

2, 3, 4, 8, 9, 32, 36, 64, 81, 100, 121, 144, 228, 256, 300, 400, 441, 468, 800, 1200, 2964, 5202, 5408, 6084, 6400, 7500, 8100, 9216, 24556, 28092, 31329, 32176, 32400, 37296, 49017, 49152, 57600, 72156, 80400, 83161, 86352, 88200, 133200

Offset: 1

N. J. A. Sloane, Sep 22 2017

nonn

Naively, one might have expected these numbers to have some other distinguishing property (primorials, perhaps), but that seems not to be the case.

Except for 3 of the listed terms, a(n)-1 or a(n)+1 has at most 2 prime divisors. The same is true for many of the terms themselves, often of the form 2^k, 3^k, 2^k*3^k' or 2^k*5^k'. (Factorization of the terms: 2, 3, 2^2, 2^3, 3^2, 2^5, 2^2*3^2, 2^6, 3^4, 2^2*5^2, 11^2, 2^4*3^2, 2^2*3*19, 2^8, 2^2*3*5^2, 2^4*5^2, 3^2*7^2, 2^2*3^2*13, 2^5*5^2, ...) - M. F. Hasler, Sep 25 2017

Hugo Pfoertner, Table of n, a(n) for n = 1..56

Cf. A039654, A039655, A292112.

m=-n=1; until(print1(n","), until(A039654(n++)>m,); m=A039654(n)) \\ M. F. Hasler, Sep 25 2017

A291776 a(n) = prime that is eventually reached when x -> sigma(x)-1 is repeatedly applied to 2^n-1, or -1 if no prime is ever reached.

Original entry on oeis.org

3, 7, 23, 31, 103, 127, 431, 911, 1847, 6719, 10487, 8191, 56999, 41399, 135647, 131071, 560159, 524287, 1999871, 3982271, 5909759, 17512991, 46092239, 46335599, 164460119, 186592247, 736727807, 3926707199, 4146049487, 2147483647, 8994904463, 11132323439

Offset: 2

N. J. A. Sloane, Aug 31 2017

nonn

			For n=9, 2^n-1 = 511 with iterates 511->591->791->911, and 911 is the first prime, so a(7)=911.

Lars Blomberg, Table of n, a(n) for n = 2..270

Cf. A039654, A039655, A291301, A291302, A291777.

P(x) = {for(c=0,10^6,if(isprime(x),return(x),x=sigma(x)-1));-1}
vector(200,n,P(2^(n+1)-1)) \\ Lars Blomberg, Sep 01 2017

Added a(7) and a(13)-a(33) from Lars Blomberg, Sep 01 2017

A291777 a(n) = number of steps to reach a prime when x -> sigma(x)-1 is repeatedly applied to 2^n-1, or -1 if no prime is ever reached.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 1, 3, 2, 9, 2, 0, 7, 3, 4, 0, 2, 0, 1, 4, 1, 4, 2, 3, 4, 2, 12, 22, 8, 0, 3, 3, 4, 3, 1, 2, 2, 3, 3, 4, 3, 13, 2, 16, 3, 8, 3, 14, 17, 9, 37, 4, 7, 4, 7, 11, 4, 3, 14, 0, 14, 8, 1, 6, 8, 73, 26, 10, 1, 32, 6, 10, 2, 6, 2, 33, 2, 4, 52, 12, 16

Offset: 2

N. J. A. Sloane, Aug 31 2017

nonn

			For n=9, 2^n-1 = 511 with iterates 511->591->791->911, and 911 is the first prime, so a(7)=3.

Lars Blomberg, Table of n, a(n) for n = 2..270

Cf. A039654, A039655, A291301, A291302, A291776.

C(x) = {for(c=0,10^5,if(isprime(x),return(c),x=sigma(x)-1));-1}
vector(200,n,C(2^(n+1)-1)) \\ Lars Blomberg, Sep 01 2017

a(13)-a(82) from Lars Blomberg, Sep 01 2017

cp's OEIS Frontend

A292113 List of numbers n such that A039654(n) reaches a new record high.

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A291776 a(n) = prime that is eventually reached when x -> sigma(x)-1 is repeatedly applied to 2^n-1, or -1 if no prime is ever reached.

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A291777 a(n) = number of steps to reach a prime when x -> sigma(x)-1 is repeatedly applied to 2^n-1, or -1 if no prime is ever reached.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Extensions