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A240563 Primes formed from concatenation of higher primes onto the previous entry until prime, starting from 2. 3
2, 23, 2311, 231131, 23113147, 23113147229, 23113147229251, 23113147229251577, 23113147229251577857, 23113147229251577857859, 23113147229251577857859911, 231131472292515778578599111123, 2311314722925157785785991111231223 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This generates a monotonically increasing sequence, nicely spread out, likely infinite. By altering the starting prime value, a family of such sequences can easily be generated.

Derived from A080155. - T. D. Noe, Apr 11 2014

From the first 155 points, with x = #digits, y = sequence pointer y~ A*x^B with (A, B) = (0.6624, 0.8106). This indicates a 100-digit prime in the vicinity of y = 28 for example. - Bill McEachen, Apr 13 2014

Only from the first 100 entries, it would appear that an upper bound on the number of digits in a(n) is A092777(n). - Bill McEachen, Sep 15 2015

LINKS

Bill McEachen, Table of n, a(n) for n = 1..100

EXAMPLE

Begin from 2.

Next we try 23 - it is prime, this sets next iteration (23 is the "constant" part), upon which we try higher primes.

Next we try 235 - composite; next we try 237 - composite; next we try 2311 - prime, this sets next iteration (2311 now becomes the "constant" part), upon which we try higher primes.

Next we try 231113 - composite; next we try 231117 - composite; ...; next we try 231131 - prime, this sets next iteration (231131 now becomes the "constant" part), upon which we try higher primes.

Next we try 23113147 - prime, this sets next iteration (23113147 now becomes the "constant" part), upon which we try higher primes.

MAPLE

X:= 2: p:= 3: a[1]:= 2:

for i from 2 to 30 do

  while not isprime(X*10^(1+ilog10(p))+p) do

     p:= nextprime(p)

  od:

  X:= X*10^(1+ilog10(p))+p;

  a[i]:= X;

  p:= nextprime(p);

od:

seq(a[i], i=1..30); # Robert Israel, Sep 15 2015

MATHEMATICA

s[1] = 2; s[n_] := s[n] = Block[{d = Flatten[IntegerDigits /@ Array[s, n-1]], p = NextPrime@s[n - 1]}, While[! PrimeQ@ FromDigits@ Join[d, IntegerDigits@p], p = NextPrime@p]; p]; a[n_] := FromDigits@ Flatten[ IntegerDigits /@ Array[s, n]]; Array[a, 10] (* Giovanni Resta, Apr 09 2014 *)

PROG

(PARI) print1(N=2); p=3; for(n=2, 10, while(!isprime(eval(Str(N, p))), p=nextprime(p+1)); N=eval(Str(N, p)); p=nextprime(p+1); print1(", "N)) \\ Charles R Greathouse IV, Apr 09 2014

CROSSREFS

Cf. A069151 (variant).

Cf. A080155 (primes used in concatenation).

Sequence in context: A239811 A082963 A083759 * A067823 A114794 A090509

Adjacent sequences:  A240560 A240561 A240562 * A240564 A240565 A240566

KEYWORD

nonn,base

AUTHOR

Bill McEachen, Apr 07 2014

EXTENSIONS

a(7)-a(13) from Giovanni Resta, Apr 09 2014

STATUS

approved

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Last modified July 10 13:04 EDT 2020. Contains 335576 sequences. (Running on oeis4.)