A240563 Primes formed from concatenation of higher primes onto the previous entry until prime, starting from 2.

2, 23, 2311, 231131, 23113147, 23113147229, 23113147229251, 23113147229251577, 23113147229251577857, 23113147229251577857859, 23113147229251577857859911, 231131472292515778578599111123, 2311314722925157785785991111231223

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