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A248370
a(n+1) is the smallest prime beyond a(n) such that a(n+1) modulo a(n) is (congruent to) a prime; start with a(0)=1.
0
1, 3, 5, 7, 17, 19, 41, 43, 89, 181, 367, 739, 1481, 1483, 2969, 2971, 5953, 11909, 23831, 23833, 47713, 95429, 190871, 381749, 763559, 1527121, 3054283, 6108607, 12217327, 24434701, 48869413, 97738843, 195477691, 390955399, 781910809, 1563821621, 3127643381, 3127643383, 6255286777
OFFSET
0,2
COMMENTS
The same terms > 3 would be obtained when starting with a(1)=2.
Shevelev cites El Bachraoui, Lemoine-Levy's conjecture and A046927, cf. links.
FORMULA
If a(n)+2 is prime, then a(n+1) = a(n)+2, else a(n+1) > 2*a(n), since a(n)+p is even for primes a(n), p > 2.
MATHEMATICA
sp[n_]:=Module[{p=NextPrime[n]}, While[!PrimeQ[Mod[p, n]], p=NextPrime[p]]; p]; Join[{1}, NestList[sp, 3, 20]] (* The program generates the first 21 terms of the sequence. To generate more, increase the constant "20" in the NestList function, but the program may take a long time to run. *) (* Harvey P. Dale, Jan 13 2019 *)
PROG
(PARI) {print1(L=3); for(p=L+1, 9e9, p=nextprime(p); isprime(p%L)&&print1(", "L=p)+(isprime(p+2)||p*=2))}
CROSSREFS
Cf. A046927.
Sequence in context: A171254 A092951 A001259 * A087126 A348438 A331800
KEYWORD
nonn
AUTHOR
Eric Angelini and M. F. Hasler, Oct 05 2014
STATUS
approved