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

1,1

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: A217933 A005594 A374681 * A347783 A079968 A280194

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