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 A285010 a(n+1) = a(n) + p, where p is the largest prime less than a(n); a(1) = 3. 1
 3, 5, 8, 15, 28, 51, 98, 195, 388, 771, 1540, 3071, 6138, 12271, 24540, 49073, 98142, 196271, 392518, 785021, 1570038, 3140045, 6280086, 12560153, 25120300, 50240589, 100481176, 200962343, 401924670, 803849309, 1607698612, 3215397195, 6430794388, 12861588761, 25723177510 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS After a(1) the sequence alternates between odd and even numbers (obviously). There is at least 1 prime between p and 2p (Bertrand), and since there is no prime between p and a(n) there must be at least one prime between a(n) and a(n) + p. Hence the sequence continues indefinitely, and each added prime is added once only. The underlying sequence of added primes is: 2, 3, 7, 13, 23, 47, 97, ...; namely A075028 or A068524 but without their initial terms (1, 2 respectively). Four primes occur in the first 24 terms, a(1) = 3, a(2) = 5, a(18) = 196271, and a(24) = 12560153, suggesting a higher density of primes here than in related sequence A123196, in which only three primes arise in the first 500 terms. It would be interesting to examine this further, once more terms become available. LINKS Giovanni Resta, Table of n, a(n) for n = 1..3000 FORMULA a(n) ~ c * 2^n, where c = 0.748642996358317338.... - Bill McEachen, May 09 2024 EXAMPLE a(1) = 3, the first odd prime. The greatest prime less than 3 is 2, so a(2) = 3 + 2 = 5. Greatest prime less than 5 is 3 so a(3) = 5 + 3 = 8. Likewise a(4) = 8 + 7 = 15; etc. MATHEMATICA a[1]=3; a[n_] := a[n] = a[n-1] + NextPrime[a[n-1], -1]; Array[a, 35] (* Giovanni Resta, Apr 10 2017 *) NestList[#+NextPrime[#, -1]&, 3, 40] (* Harvey P. Dale, Aug 22 2020 *) PROG (PARI) lista(nn) = { print1(a=3, ", "); for (n=2, nn, a += precprime(a-1); print1(a, ", "); ); } \\ Michel Marcus, Apr 08 2017 CROSSREFS Cf. A123196, A075058, A068524. Sequence in context: A191633 A215327 A208723 * A352917 A099846 A141775 Adjacent sequences: A285007 A285008 A285009 * A285011 A285012 A285013 KEYWORD easy,nonn AUTHOR David James Sycamore, Apr 07 2017 EXTENSIONS More terms from Michel Marcus, Apr 08 2017 STATUS approved

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Last modified September 13 08:33 EDT 2024. Contains 375902 sequences. (Running on oeis4.)