|
%I #59 Oct 16 2015 17:35:43
%S 2,23,2311,231131,23113147,23113147229,23113147229251,
%T 23113147229251577,23113147229251577857,23113147229251577857859,
%U 23113147229251577857859911,231131472292515778578599111123,2311314722925157785785991111231223
%N Primes formed from concatenation of higher primes onto the previous entry until prime, starting from 2.
%C 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.
%C Derived from A080155. - _T. D. Noe_, Apr 11 2014
%C 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
%C 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
%H Bill McEachen, <a href="/A240563/b240563.txt">Table of n, a(n) for n = 1..100</a>
%e Begin from 2.
%e Next we try 23 - it is prime, this sets next iteration (23 is the "constant" part), upon which we try higher primes.
%e 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.
%e 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.
%e Next we try 23113147 - prime, this sets next iteration (23113147 now becomes the "constant" part), upon which we try higher primes.
%p X:= 2: p:= 3: a[1]:= 2:
%p for i from 2 to 30 do
%p while not isprime(X*10^(1+ilog10(p))+p) do
%p p:= nextprime(p)
%p od:
%p X:= X*10^(1+ilog10(p))+p;
%p a[i]:= X;
%p p:= nextprime(p);
%p od:
%p seq(a[i],i=1..30); # _Robert Israel_, Sep 15 2015
%t 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 *)
%o (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
%Y Cf. A069151 (variant).
%Y Cf. A080155 (primes used in concatenation).
%K nonn,base
%O 1,1
%A _Bill McEachen_, Apr 07 2014
%E a(7)-a(13) from _Giovanni Resta_, Apr 09 2014
| 