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 A219271 Primes such that concatenating successors results in primes five successive times. 1
 352367441, 4709250017, 16653466069, 23908162969, 51658610299, 52042712083, 53924700541, 54540661141, 64499058697, 84398639471, 100000699399, 161578812517, 169226036407, 194345988607, 201952832951 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 6 05:18 EDT 2021. Contains 343580 sequences. (Running on oeis4.)