A161849 -id:A161849 - cp's OEIS frontend

A161965 Composite numbers in A161849 in the order of appearance.

4, 6, 4, 4, 6, 8, 4, 6, 6, 4, 10, 9, 4, 6, 4, 4, 4, 4, 8, 4, 10, 4, 12, 14, 4, 4, 10, 4, 6, 9, 12, 8, 6, 4, 4, 6, 6, 6, 4, 18, 8, 4, 9, 4, 4, 9, 4, 14, 9, 4, 6, 6, 18, 8, 4, 6, 20, 4, 6, 8, 15, 4, 10, 4, 4, 9, 8, 4, 16, 4, 6, 4, 6, 8, 6, 12, 4, 10, 4, 14, 4, 6, 6, 10, 10, 10, 12, 12, 4, 14, 4, 18, 16

Offset: 1

Juri-Stepan Gerasimov, Jun 23 2009

			The sequence shows a(1) = A161849(55)=4, a(2)=A161849(66) = 6,
a(3) = A161849(70)=4 etc.

Cf. A002808, A052369, A056608.

Definition simplified, sequence extended by R. J. Mathar, Sep 11 2009

A161966 Primes in A161849 in order of appearance.

Original entry on oeis.org

2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 3, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 7, 2, 2, 3, 5, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 5, 2, 2, 3, 3, 2, 2, 5, 2, 2, 3, 2, 2, 11, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 5, 3, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 3

Offset: 1

Juri-Stepan Gerasimov, Jun 23 2009

nonn

A052369(k) mod A056608(k) where prime.

The remainder of the division of the largest by the smallest prime divisor of the k-th composite, discarding all nonprime results, as k increases.

			The first seven entries of A161849 are not prime, and a(1)=A161849(8)=2 is the first one selected.
The entries A161849(9..20) are not prime, and a(2)=A161849(21) is the next one selected.

Cf. A002808, A052369, A056608.

Edited and extended by R. J. Mathar, Aug 02 2009

A161986 a(n) = k+r where k is composite(n) and r is (largest prime divisor of k) mod (smallest prime divisor of k).

Original entry on oeis.org

4, 7, 8, 9, 11, 13, 15, 17, 16, 19, 21, 22, 23, 25, 25, 27, 27, 29, 31, 32, 35, 35, 37, 37, 39, 40, 41, 43, 45, 47, 47, 49, 49, 51, 53, 53, 55, 56, 57, 58, 59, 61, 63, 64, 64, 68, 67, 69, 71, 71, 73, 75, 77, 77, 81, 79, 81, 81, 83, 85, 87, 87, 89, 89, 91, 97, 93, 94, 95, 99, 97

Offset: 1

Klaus Brockhaus, Jun 23 2009

nonn

Auxiliary sequence for A161850, which is the subsequence consisting of all terms that are prime.

a(n) = A002808(n)+A161849(n).

			n = 1: composite(1) = 4; (largest prime divisor of 4) = (smallest prime divisor 4) = 2; 2 mod 2 = 0. Hence a(1) = 4+0 = 4.
n = 5: composite(5) = 10; (largest prime divisor of 10) = 5; (smallest prime divisor 10) = 2; 5 mod 2 = 1. Hence a(5) = 10+1 = 11.

Bill McEachen, Table of n, a(n) for n = 1..10000

Cf. A161850, A002808 (composite numbers), A052369 (largest prime factor of n-th composite), A056608 (smallest divisor of n-th composite), A161849 (A052369(n) mod A056608(n)).

[ n + D[ #D] mod D[1]: n in [2..100] | not IsPrime(n) where D is PrimeDivisors(n) ];

genit(maxx=1000)={ctr=0;arr=List();forcomposite(k=4,+oo,v=factor(k)[,1];r=v[#v]%v[1];ctr+=1;if(ctr>=maxx,break);listput(arr,k+r));arr} \\ Bill McEachen, Nov 17 2021

A161850 Subsequence of A161986 consisting of all terms that are prime.

Original entry on oeis.org

7, 11, 13, 17, 19, 23, 29, 31, 37, 37, 41, 43, 47, 47, 53, 53, 59, 61, 67, 71, 71, 73, 79, 83, 89, 89, 97, 97, 101, 101, 103, 107, 109, 113, 127, 131, 137, 137, 139, 149, 149, 151, 157, 163, 163, 167, 167, 173, 179, 179, 181, 193, 191, 193, 197, 199, 211, 223, 227

Offset: 1

Juri-Stepan Gerasimov, Jun 20 2009

nonn

A161986(n) = k+r where k is n-th composite and r is remainder of (largest prime divisor of k) divided by (smallest prime divisor k).

			A161986(1) to A161986(27) are 4, 7, 8, 9, 11, 13, 15, 17, 16, 19, 21, 22, 23, 25, 25, 27, 27, 29, 31, 32, 35, 35, 37, 37, 39, 40, 41. Hence a(1) to a(11) are the prime terms among them, namely 7, 11, 13, 17, 19, 23, 29, 31 ,37, 37, 41.

Cf. A161986 (A002808(n)+A161849(n)), A002808 (composite numbers), A161849 (A052369(n) mod A056608(n)), A052369 (largest prime factor of n-th composite), A056608 (smallest divisor of n-th composite).

[ p: n in [2..230] | not IsPrime(n) and IsPrime(p) where p is n+D[ #D] mod D[1] where D is PrimeDivisors(n) ];

Edited and corrected (a(19)=57 replaced by 67; a(38)=137, a(49)=179, a(50)=179 inserted) by Klaus Brockhaus, Jun 24 2009

cp's OEIS Frontend

A161965 Composite numbers in A161849 in the order of appearance.

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A161966 Primes in A161849 in order of appearance.

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A161986 a(n) = k+r where k is composite(n) and r is (largest prime divisor of k) mod (smallest prime divisor of k).

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A161850 Subsequence of A161986 consisting of all terms that are prime.

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