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A230086 Lexicographically earliest permutation of the positive integers such that a(n+a(n)) is prime for all n. 0
1, 2, 3, 5, 4, 7, 6, 8, 11, 9, 10, 12, 13, 14, 15, 17, 16, 18, 19, 23, 29, 20, 21, 31, 22, 37, 24, 41, 25, 43, 26, 27, 47, 28, 30, 53, 32, 59, 33, 34, 35, 61, 67, 71, 36, 38, 73, 39, 40, 79, 83, 42, 44, 89, 97, 45, 101, 46, 103, 48, 49, 107, 109, 50 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

"Lexicographically earliest" means that a(n) is chosen as small as possible, in the order of increasing n, without leading to a contradiction. "Permutation" means that no integer may appear more than once, and together with the former prescription, every integer will indeed appear.

Existence of the sequence is guaranteed since terms can be filled in one after the other, and each time the place n+a(n) (which comes later) is required to be filled with a prime. This does not prevent from filling other places with primes. Since at each step the smallest available number is used, the primes as well as the composites appear in their natural order.

It appears that the primes are exactly the "early birds" of this sequence, i.e., the terms such that a(n)>n, except for {2, 3, 13, 19} which appear in their natural position. - M. F. Hasler, Oct 09 2013

LINKS

Table of n, a(n) for n=1..64.

E. Angelini, a(a(n) + n) is prime, SeqFan list, Oct 08 2013

Index to the OEIS: Entries related to self-referencing sequences.

PROG

(PARI) {u=0; a=vector(1000); for(i=1, #a, a[i]>0 && next; for(x=1, 9e9, (!a[i] || isprime(x)) && !bittest(u, x) && (a[i]=x) && break); u+=1<<a[i]; i+a[i]<=#a && a[i+a[i]]=-1); vecextract(a, "..100")}

CROSSREFS

Sequence in context: A098313 A098311 A342265 * A333404 A227082 A227142

Adjacent sequences:  A230083 A230084 A230085 * A230087 A230088 A230089

KEYWORD

nonn

AUTHOR

Eric Angelini and M. F. Hasler, Oct 08 2013

STATUS

approved

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Last modified July 25 10:07 EDT 2021. Contains 346289 sequences. (Running on oeis4.)