A123196 a(1) = 2; a(n+1) = a(n) + p, where p is the largest prime <= a(n).

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

Offset: 1

Author

Peter C. Heinig (algorithms(AT)gmx.de), Oct 04 2006

Keywords

• easy
• nonn

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)

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..3322

Crossrefs

Cf. A075058, A068524.

Programs

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 *)

PARI

lista(nn) = { print1(a=2, ", "); for (n=2, nn, na = a + precprime(a); print1(na, ", "); a = na;);} \\ Michel Marcus, Apr 08 2017

Extensions

New name from David James Sycamore, Apr 07 2017