OFFSET
0,2
COMMENTS
The even places a(0),a(2),... are to be filled with nonprime numbers. The term a(2) between a(1)=2 and a(3)=3 can only be zero, therefore the smallest possible sequence starts (1,2,0,3,...). The number 1 cannot appear elsewhere than in the initial position 0. The sequence cannot be a permutation of the integers, since the number 4 cannot appear anywhere: if prime(n)+4 is prime (n>2), then this is necessarily prime(n+1) and congruent to 5 modulo 6, so prime(n+1)+4 cannot be prime. There is also no odd composite number in the sequence.
LINKS
M. F. Hasler, Table of n, a(n) for n = 0..9999
E. Angelini, Primes and prime sums, SeqFan mailing list, Jan 14 2013
Jean-Marc Falcoz, Primes and prime sums
J.-M. Falcoz, Primes and prime sums [Cached copy, with permission]
PROG
(PARI) {print1("1, "q=2); u=2 /*bitmap of used even numbers*/; forprime(p=3, default(primelimit), forstep(i=0, 9e9, 2, !bittest(u, i\2) & isprime(q+i) & isprime(p+i) & (1+q=i) & break); u+=1<<(q\2); print1(", "q", "p); q=p)}
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Eric Angelini and M. F. Hasler, Jan 14 2013
STATUS
approved