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 A123196 a(1) = 2; a(n+1) = a(n) + p, where p is the largest prime <= a(n). 2
 2, 4, 7, 14, 27, 50, 97, 194, 387, 770, 1539, 3070, 6137, 12270, 24539, 49072, 98141, 196270, 392517, 785020, 1570037, 3140044, 6280085, 12560152, 25120299, 50240588, 100481175, 200962342, 401924669, 803849308, 1607698611, 3215397194 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Old Name was: Jumping along the natural numbers, starting at the first prime and letting the greatest prime reached so far determine the length of the next jump, when "reached" is defined as "jumped over" as well as "landed on". Note that the infinitude of this sequence follows from Bertrand's postulate. From David James Sycamore, Apr 07 2017: (Start) Among the first 500 terms, the primes are a(1)=2, a(3)=7, a(7)=97, a(107)=121474271192355984857330583869867, a(131), a(213), a(263), and a(363). The underlying sequence of added primes is A075058 and A068524, without their first terms (1 & 2 respectively). (End) LINKS Giovanni Resta, Table of n, a(n) for n = 1..3322 EXAMPLE a(1)=2 since 2 is the first prime. a(3)=7 since having landed at 4, the greatest prime reached so far is 3. a(8)=194=97+97 since with the preceding term we had landed on a prime. a(17)=98141 since having passed the prime 49069 with the term a(16) but not having reached the prime 49081, we have to add the former and indeed 98141=49069+49072. MAPLE a[1]:=2; for k from 1 to 29 do x:=a[k]: if isprime(x) then a[k+1]:=x+x: else y:=x: while not(isprime(y)) do y:=y-1:od; a[k+1]:= x+y: fi; od; MATHEMATICA a[1]=2; a[n_]:= a[n] = If[PrimeQ[a[n-1]], 2 a[n-1], a[n-1] + NextPrime[ a[n-1], -1]]; Array[a, 100] (* Giovanni Resta, Apr 08 2017 *) PROG (PARI) lista(nn) = { print1(a=2, ", "); for (n=2, nn, na = a + precprime(a); print1(na, ", "); a = na; ); } \\ Michel Marcus, Apr 08 2017 CROSSREFS Cf. A075058, A068524. Sequence in context: A224960 A217933 A005594 * A079968 A280194 A001631 Adjacent sequences:  A123193 A123194 A123195 * A123197 A123198 A123199 KEYWORD easy,nonn AUTHOR Peter C. Heinig (algorithms(AT)gmx.de), Oct 04 2006 EXTENSIONS New name from David James Sycamore, Apr 07 2017 STATUS approved

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Last modified February 23 06:13 EST 2020. Contains 332159 sequences. (Running on oeis4.)