The On-Line Encyclopedia of Integer Sequences (OEIS)

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A334885

Let q = p | p' be the digit concatenation of a prime p with its prime successor. If the result is a prime repeat the construction setting p = q. a(n) is the smallest prime for which this can be repeated exactly n times.
(history; published version)

#10 by Alois P. Heinz at Tue May 26 22:22:16 EDT 2020

STATUS

editing

approved

#9 by Alois P. Heinz at Tue May 26 22:20:52 EDT 2020

NAME

Let q = p | p' be the digit concatenation of a prime p with its prime successor. If the result is a prime repeat the construction setting p = q. a(kn) is the smallest prime for which this can be repeated exactly k n times.

STATUS

proposed

editing

Discussion

Tue May 26

22:21

Alois P. Heinz: n is the index of a sequence, so you can write a(n).

#8 by Giovanni Resta at Mon May 18 05:06:03 EDT 2020

STATUS

editing

proposed

#7 by Giovanni Resta at Mon May 18 05:06:00 EDT 2020

NAME

Let q = p | p' be the digit concatenation of a prime p with its prime successor. If the result is a prime repeat the construction setting p = q. a(k) is the smallest prime number for which the operation of concatenating a number with the next prime this can be repeated exactly k times, obtaining each time a prime number.

STATUS

proposed

editing

#6 by Michel Marcus at Thu May 14 10:18:43 EDT 2020

STATUS

editing

proposed

Discussion

Sun May 17

02:24

Peter Luschny: The name is OK, even if decoding is a little difficult. A possible alternative would be a more explanatory style.

02:25

Peter Luschny: Let q = p | p' be the digit concatenation of a prime p 
with its prime successor. If the result is a prime repeat 
the construction with q. a(k) is the smallest prime which 
in this way can be extended k times but not more often.

#5 by Michel Marcus at Thu May 14 10:18:40 EDT 2020

LINKS

Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_029.htm">Puzzle 29. P_i = P_(i-1) & nxtprm(P_(i-1)), P_i = prime for i => 1</a>, The Prime Puzzles and Problems Connection.

STATUS

proposed

editing

#4 by Giovanni Resta at Thu May 14 10:16:23 EDT 2020

STATUS

editing

proposed

#3 by Giovanni Resta at Thu May 14 09:28:09 EDT 2020

COMMENTS

a(6) > 10^13.

Discussion

Thu May 14

09:28

Giovanni Resta: I'm open to suggestions regarding the Name...

#2 by Giovanni Resta at Thu May 14 09:27:10 EDT 2020

NAME

allocated a(k) is the smallest prime number for Giovanni Restawhich the operation of concatenating a number with the next prime can be repeated exactly k times, obtaining each time a prime number.

DATA

3, 2, 13681, 467, 127787377, 200603842261

OFFSET

0,1

LINKS

Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_029.htm">Puzzle 29. P_i = P_(i-1) & nxtprm(P_(i-1)), P_i = prime for i => 1</a>

EXAMPLE

Let "|" denote concatenation.

3 | 5 = 35, which is not prime, so a(0) = 3.

2 | 3 = 23 (prime), 23 | 29 = 2329 (composite), so a(1) = 2.

13681 | 13687 (prime), 1368113687 | 1368113699 (prime), 13681136871368113699 | 13681136871368113711 (composite), so a(2) = 13681.

MATHEMATICA

a[n_] := Block[{pp=1, p, q, c=-1}, While[ c!=n, c=0; p = pp = NextPrime@ pp; While[ PrimeQ[ q = FromDigits[ Join @@ IntegerDigits@{p, NextPrime@ p}]], c++; p = q]]; pp]; a /@ Range[0, 3]

CROSSREFS

Cf. A030459, A034593, A036339, A036340, A036341.

KEYWORD

allocated

nonn,base,more

AUTHOR

Giovanni Resta, May 14 2020

STATUS

approved

editing

#1 by Giovanni Resta at Thu May 14 09:27:10 EDT 2020

NAME

allocated for Giovanni Resta

KEYWORD

allocated

STATUS

approved