A162662 Sequence of alternating increasing odd and increasing even numbers such that the sum of any two terms of opposite parity is a prime number.

1, 2, 3, 4, 9, 10, 27, 70, 57, 100, 267, 1060, 1227, 27790, 1479, 146380, 3459, 2508040, 49527, 35506900, 470079

Offset: 1

Author

Michel Lagneau, Jan 27 2011

Keywords

• nonn
• more

Comments

a(n+1) is taken to be the smallest number, greater than a(n-2), of opposite parity to a(n) that satisfies the condition.

A000034: Period 2: repeat [1, 2] is another sequence satisfying the definition without the increasing constraint. - Michel Marcus, Dec 22 2014

Examples

			1060 + 267 = 1327 is prime;
1060 + 27 = 1087 is prime;
1060 + 9 = 1069 is prime;
1060 + 3 = 1063 is prime;
1060 + 1 = 1061 is prime.
		

Crossrefs

Cf. A180743, A115760.

Programs

Maple

with(numtheory):nn:=30:T:=array(1..nn): T[1]:=1:a:=1:for k from 2 to nn do:id:=0:for
  n from k to 1000000 while(id=0) do:n1:=irem(n,2):i:=0:for p from 1 to a do:
  if n=T[p] then i:=0:else fi: x:=n+T[p]:if type(x, prime)=true then i:=i+1:else
  fi:od: if i=ceil(a/2) then T[k]:=n:print(n):a:=a+1:id:=1:else fi:od:od:

PARI

ok(k, m, v) = {if (k % 2, js = 2, js = 1); forstep(j=js, m, 2, if (! isprime(k + v[j]), return (0));); return (1);}
findval(n, v) = {if (n <=2, k = n, k = v[n-2]+2); while (!ok (k, n-1, v), k+= 2); k;}
lista(nn) = {a = vector(nn); a[1] = 1; print1(a[1], ", "); for (n=2, nn, a[n] = findval(n, a); print1(a[n], ", "););} \\ Michel Marcus, Dec 22 2014

Extensions

a(18)-a(21) from Michel Marcus, Dec 22 2014

Name clarified by Michel Marcus, Dec 22 2014