A182164 Start with a(1)=1, if a(n) is prime, jump over a(n) neighbors to the left, else to the right. Fill in the largest possible unused prime, or the least unused composite, such that the next destination is not yet filled.

1, 6, 4, 10, 8, 9, 14, 5, 3, 26, 18, 12, 22, 7, 2, 11, 27, 16, 34, 28, 50, 15, 24, 35, 17, 39, 51, 57, 38, 20, 45, 32, 44, 87, 23, 21, 13, 19, 94, 48, 69, 72, 62, 93, 30, 63, 65, 25, 31, 58, 37, 80, 54, 29, 102, 96, 82, 47, 77, 36, 90, 114, 153, 138, 33, 40, 117, 41, 106, 68, 134

Offset

1,2

Comments

"Largest possible" means that the prime has to be less than n-1 (to be able to jump over a(n) neighbors to the left) and the place at index n-a(n)-1 has to be vacant. If (and only if) no such prime exists, the "or" clause (filling with composite) applies.

Links

M. F. Hasler, Table of n, a(n) for n = 1..313

E. Angelini, Jumping back and forth (primes and composites), SeqFan list, Apr 15 2012

Prog

(PARI) A182164_list(N_min, debug)= my(L=1 /* least unfilled position */, p=1 /* current position */, u=0 /* used numbers (bitmap) */, a=vector(7*N_min)); a[1]=1; while( while (a[L] , L++) || L<N_min, p += (a[p]+1) * (-1)^isprime(a[p]); forstep( t=p-L, 2, -1, t=precprime(t); !bittest(u, t) && !a[p-t-1] && (u+=1<<a[p]= t) && next(2)); for (t=4, 9e9, bittest(u, t) && next; isprime(t) && next; #a>p+t || a=concat(a, vector(p+t+1-#a)); a[p+t+1] && next; u+=1<<a[p]=t; break)); debug && print("Largest used: ", #a); vecextract(a, 2^(L-1)-1)

Crossrefs

Sequence in context: A143520 A075450 A145979 * A294093 A257926 A116946

Adjacent sequences: A182161 A182162 A182163 * A182165 A182166 A182167

Keyword

nonn

Author

Eric Angelini and M. F. Hasler, Apr 15 2012

Status

approved