A226291 Least positive integer which starts a chain of exactly n primes under the map p -> p+p'+p'', where p' = least prime > p.

1, 2, 17, 11, 5, 7, 2543, 249217, 1783841, 2494517, 624921844601, 507995698619

Offset

0,2

Comments

Restricting the terms to be odd primes, the initial term would be a(1)=3.

Links

Table of n, a(n) for n=0..11.

J. K. Andersen, Curio for 507995698619, in C. Caldwell's "prime pages".

P. Carmody, three-prime sum chains, "primenumbers" group on Yahoo!

Phil Carmody, Jens Kruse Andersen and others, three-prime sum chains, digest of 7 messages in primenumbers Yahoo group, Jun 2 - Jun 4, 2013.

Carlos Rivera, Puzzle 421. Staircase of consecutive primes, The Prime Puzzles & Problems Connection.

Example

Let f(x)=x+x'+x'', where x' = nextprime(x), the next larger prime.
Depending on the starting value, we get:
1 (not prime): 0 primes in the chain (as with any other composite starting value), a(0)=1.
2 -> f(2) = 2+3+5 = 10 (not prime): chain of 1 prime, a(1) = 2.
3 -> f(3) = 3+5+7 = 15 (not prime): chain of 1 prime.
5 -> f(5) = 5+7+11 = 23 -> f(23) = 23+29+31 = 83 -> f(83) = 269 -> 817 (not prime): chain of 4 primes, a(4)=5.
7 -> 31 -> 109 -> 349 -> 1061 -> 3193  (not prime): chain of 5 primes, a(5)=7.
11 -> 41 -> 131 -> 407 (not prime): chain of 3 primes, a(3)=11.
13 -> 49 (not prime): chain of 1 prime.
17 -> 59 -> 187 (not prime): chain of 2 primes: a(2) = 17.

Prog

(PARI) a(n)={n>1&&forprime(p=1, , my(pp=p); for(i=0, n, isprime(pp=pp+0+nextprime(1+pp=nextprime(pp+1))+pp)==(i<n)||next(2)); return(p)); 2}

Crossrefs

Sequence in context: A055677 A362397 A257466 * A359437 A077311 A196732

Adjacent sequences: A226288 A226289 A226290 * A226292 A226293 A226294

Keyword

nonn

Author

M. F. Hasler, Jun 02 2013

Status

approved