cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A080156 Values of n corresponding to the terms in sequence A080155. For any k, the concatenation of the a(1) to a(k)-th primes is prime and each value of k is the smallest for which this is true.

Original entry on oeis.org

1, 2, 5, 11, 15, 50, 54, 106, 148, 149, 156, 188, 200, 211, 248, 326, 359, 374, 417, 467, 699, 798, 891, 966, 1038, 1519, 1542, 1578, 1831, 1908, 1982, 2079, 2305, 2640, 2660, 2845, 3078, 3145, 3760, 3777, 3835, 4538, 4630, 4991, 5019, 5554, 5658, 5827
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003

Keywords

Links

Crossrefs

Cf. A073640, A080152-A080155.

Programs

  • Maple
    with(numtheory): pout := [2]: nout := [1]: for n from 2 to 5000 do: p := ithprime(n): d := parse(cat(seq(pout[i],i=1..nops(pout)),p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od: nout;

Formula

a(n) = prime(A080155(n)).

Extensions

Edited by Charles R Greathouse IV, Apr 30 2010

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

Original entry on oeis.org

2, 23, 2311, 231131, 23113147, 23113147229, 23113147229251, 23113147229251577, 23113147229251577857, 23113147229251577857859, 23113147229251577857859911, 231131472292515778578599111123, 2311314722925157785785991111231223
Offset: 1

Views

Author

Bill McEachen, Apr 07 2014

Keywords

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

Examples

			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.

Links

Crossrefs

Cf. A069151 (variant).
Cf. A080155 (primes used in concatenation).

Programs

  • 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 *)
  • 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

Extensions

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

A049462 a(n) is the smallest n-digit prime p such that the concatenation a(1)a(2)...a(n-1)p is prime, with a(1) = 2.

Original entry on oeis.org

2, 11, 151, 1013, 10867, 100673, 1000357, 10000931, 100000213, 1000000901, 10000001797, 100000000283, 1000000001911, 10000000012553, 100000000006087, 1000000000011317, 10000000000003471, 100000000000017431
Offset: 1

Views

Author

Jeff Heleen, Oct 13 2003

Keywords

Comments

The corresponding primes are certified for 44 < n < 60 (for the first 15 titanic primes). - Metin Sariyar, Oct 23 2020

Examples

			Starting with an initial prime of 2, next the smallest 2-digit prime which gives a prime is 11 (211, a prime), then 151 (3-digit prime) is the smallest to make 211151 a prime, etc.

Links

Crossrefs

Cf. A080155, A083758.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; a[1] = 2; a[n_] := a[n] = Block[{p = Sum[ a[i]*10^(n(n + 1)/2 - i(i + 1)/2), {i, 1, n - 1}], q = NextPrim[10^(n - 1)]}, While[ !PrimeQ[p + q], q = NextPrim[q]]; q]; Table[ a[n], {n, 1, 19}] (* Robert G. Wilson v, Oct 18 2003 *)

Extensions

More terms from Robert G. Wilson v, Oct 18 2003
Showing 1-3 of 3 results.

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