A219271 Primes such that concatenating successors results in primes five successive times.

352367441, 4709250017, 16653466069, 23908162969, 51658610299, 52042712083, 53924700541, 54540661141, 64499058697, 84398639471, 100000699399, 161578812517, 169226036407, 194345988607, 201952832951

Offset

1,1

Comments

a(11) itself is the primary source of interest for this particular sequence, since already at a(4) we have the first value permitting concatenation of a 7th prime. A219677 contains the sequence where successors are placed in sequence to the left rather than the right.

Links

Table of n, a(n) for n=1..15.

C. Rivera, PrimePuzzles.Net, Puzzle 708 Find sets of k consecutive primes such that ...

Example

The 72-digit prime 10000069939910000699417100000699439100000699453100000699517100000699543 is the concatenation of 6 successive primes, and deletion from the right results in a shorter prime for all 5 steps.  So, 100000699399 is one of the terms of this sequence, a(11).

Prog

(PARI) /* Output is a vector of 6 consecutive primes for each element of the sequence, the 1st of these primes. */
{
\\ This program first checks for consistency mod 3\\
p=[5, 7, 11, 13, 17, 19]; e=[10, 100, 100, 100, 100];
while(1,
if((p[1]+p[2])%3, f=1; for(i=2, 5,
if((p[i]+p[i+1])%3, f=0; break()));
if(f, P=p[1]*e[1]+p[2]; if(ispseudoprime(P),
for(i=2, 5, P*=e[i]; P+=p[i+1]; if(ispseudoprime(P)==0,
f=0; break())); if(f, print(p)))));
for(i=1, 5, p[i]=p[i+1]); p(6)=nextprime(p[6]+1);
for(i=1, 4, e[i]=e[i+1]); if(p[6]>e[5], e[5]*=10))
}
(PARI) is(n)=my(p=n); if(!ispseudoprime(p), return(0)); for(i=1, 5, n=eval(Str(n, p=nextprime(p+1))); if(!ispseudoprime(n), return(0))); 1 \\ Charles R Greathouse IV, Oct 06 2013

Crossrefs

Cf. A219677.

Sequence in context: A186628 A032757 A288273 * A167517 A227642 A189124

Adjacent sequences: A219268 A219269 A219270 * A219272 A219273 A219274

Keyword

nonn,base

Author

James G. Merickel, Nov 17 2012

Extensions

Terms missing (5 of 11) added by James G. Merickel, Jul 20 2013

Typo in a(9) fixed by James G. Merickel, Oct 06 2013

a(12)-a(15) from Charles R Greathouse IV, Oct 10 2013

Status

approved