A075594 -id:A075594 - cp's OEIS frontend

A103825 Choose a(n) to be the smallest number not yet used such that: a(1) = 1, a(2n) = composite, a(2n+1) = prime and partial sums are alternately prime or composite.

1, 4, 3, 9, 5, 15, 2, 8, 7, 25, 11, 49, 13, 21, 17, 33, 19, 27, 23, 39, 29, 119, 31, 77, 37, 35, 41, 51, 43, 45, 47, 55, 53, 57, 59, 91, 61, 65, 67, 87, 71, 69, 73, 93, 79, 85, 83, 95, 89, 63, 97, 81, 101, 99, 103, 75, 107, 105, 109, 141, 113, 115, 127, 125, 131, 111, 137

Offset: 1

Ray Chandler Feb 16 2005

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A075593, A075594, A103824.

N:= 1000: # for terms before the first term > N
Avail:= [$2..N]:
A[1]:= 1: T:= 1:
for n from 2 while assigned(A[n-1]) do
  for j from 1 to N+1-n do
    x:= Avail[j];
    if (n::even and isprime(x+T) and not isprime(x)) or
       (n::odd and isprime(x) and not isprime(x+T)) then
      A[n]:= x; T:= T+x;
      Avail:= subsop(j=NULL, Avail);
      break
    fi
  od
od:
seq(A[i],i=1..n-2); # Robert Israel, Nov 26 2020

Definition corrected by Zak Seidov, Feb 20 2005

A075593 a(1) = 1, a(2n) = prime, a(2n+1) = composite and sum of two successive terms is alternately composite or prime.

Original entry on oeis.org

1, 3, 4, 2, 9, 5, 6, 19, 10, 11, 8, 7, 12, 13, 16, 17, 14, 31, 22, 23, 18, 37, 24, 41, 20, 29, 30, 47, 26, 43, 28, 53, 36, 59, 38, 61, 40, 71, 32, 67, 34, 83, 44, 73, 54, 79, 48, 97, 42, 101, 50, 103, 46, 89, 60, 109, 58, 107, 56, 113, 66, 137, 62, 127, 52, 131, 68, 139, 72

Offset: 1

Amarnath Murthy, Sep 27 2002

nonn

This is not a permutation of the positive integers; odd composites > 9 will not appear in the sequence. - Klaus Brockhaus, Feb 06 2006

Cf. A075594, A103824, A103825.

Extended by Ray Chandler Feb 16 2005

A103824 Choose a(n) to be the smallest number not yet used such that: a(1) = 1, a(2n) = prime, a(2n+1) = composite and partial sums are alternately composite or prime.

Original entry on oeis.org

1, 3, 9, 2, 4, 5, 35, 7, 65, 11, 15, 13, 21, 17, 25, 19, 55, 23, 49, 29, 91, 31, 27, 37, 115, 41, 77, 43, 121, 47, 85, 53, 125, 59, 39, 61, 33, 67, 133, 71, 143, 73, 119, 79, 95, 83, 81, 89, 145, 97, 51, 101, 99, 103, 45, 107, 57, 109, 87, 113, 69, 127, 75, 131, 111, 137

Offset: 1

Ray Chandler Feb 16 2005

nonn

Cf. A075593, A075594, A103825.

Definition corrected by Zak Seidov, Feb 20 2005

A103934 Choose a(n) to be the smallest odd number not yet used such that: a(1) = 1, a(2n) = prime, a(2n+1) = composite and partial sums are alternately composite or prime.

Original entry on oeis.org

1, 3, 9, 5, 25, 7, 21, 11, 15, 13, 27, 17, 39, 19, 45, 23, 33, 29, 55, 31, 35, 37, 57, 41, 49, 43, 119, 47, 51, 53, 91, 59, 77, 61, 125, 67, 143, 71, 69, 73, 65, 79, 63, 83, 75, 89, 121, 97, 81, 101, 99, 103, 87, 107, 117, 109, 135, 113, 93, 127, 111, 131, 129, 137, 115, 139

Offset: 1

Ray Chandler Feb 21 2005, based on a suggestion from Zak Seidov

nonn

Cf. A075593, A075594, A103824, A103825, A103935.

A103935 Choose a(n) to be the smallest odd number not yet used such that: a(1) = 1, a(2n) = composite, a(2n+1) = prime and partial sums are alternately composite or prime.

Original entry on oeis.org

1, 9, 3, 15, 13, 21, 5, 25, 11, 27, 7, 33, 23, 35, 29, 39, 17, 45, 31, 49, 19, 51, 61, 55, 37, 57, 43, 63, 53, 65, 41, 69, 71, 75, 79, 77, 73, 81, 59, 85, 47, 87, 103, 91, 83, 93, 113, 95, 109, 99, 127, 105, 149, 111, 139, 115, 89, 117, 107, 119, 97, 121, 131, 123, 67, 125

Offset: 1

Ray Chandler Feb 21 2005, based on a suggestion from Zak Seidov

nonn

Cf. A075593, A075594, A103824, A103825, A103934.

A179485 Sums of two successive primes s such that s+-3 are primes.

Original entry on oeis.org

8, 100, 1120, 1220, 1300, 2240, 2380, 2414, 3536, 3634, 4906, 4940, 5566, 5740, 6706, 7240, 8864, 9224, 9394, 10136, 10850, 12040, 12476, 12586, 12920, 13180, 13334, 13754, 14630, 14720, 15134, 16270, 17710, 18430, 18800, 19916, 21014, 21320

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 16 2010

nonn

Intersection of A001043 and A087695. - Robert Israel, Oct 25 2017

			3+5=8,8-3=5(prime),8+3=11(prime),..

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A074924, A074925, A167597, A176984, A176986, A075593, A075594, A116360, A076565

Cf. A001043, A087695.

q:= 2; p:= 3;
count:= 0:
while count < 100 do
  q:= p; p:= nextprime(p);
  s:= q+p;
  if isprime(s-3) and isprime(s+3) then
    count:= count+1; A[count]:= s;
  fi
od:
seq(A[i],i=1..count); # Robert Israel, Oct 25 2017

q=3;Select[Table[Prime[n]+Prime[n+1],{n,7!}],PrimeQ[ #-q]&&PrimeQ[ #+q]&]
Select[Total/@Partition[Prime[Range[1400]],2,1],AllTrue[#+{3,-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 04 2018 *)

cp's OEIS Frontend

A103825 Choose a(n) to be the smallest number not yet used such that: a(1) = 1, a(2n) = composite, a(2n+1) = prime and partial sums are alternately prime or composite.

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A075593 a(1) = 1, a(2n) = prime, a(2n+1) = composite and sum of two successive terms is alternately composite or prime.

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Extensions

A103824 Choose a(n) to be the smallest number not yet used such that: a(1) = 1, a(2n) = prime, a(2n+1) = composite and partial sums are alternately composite or prime.

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Extensions

A103934 Choose a(n) to be the smallest odd number not yet used such that: a(1) = 1, a(2n) = prime, a(2n+1) = composite and partial sums are alternately composite or prime.

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Author

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Crossrefs

A103935 Choose a(n) to be the smallest odd number not yet used such that: a(1) = 1, a(2n) = composite, a(2n+1) = prime and partial sums are alternately composite or prime.

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Author

Keywords

Crossrefs

A179485 Sums of two successive primes s such that s+-3 are primes.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica