A048549 -id:A048549 - cp's OEIS frontend

A048553 a(n+1) is next smallest prime beginning with a(n), initial prime is 11.

11, 113, 11311, 113111, 1131113, 11311133, 1131113353, 113111335313, 11311133531339, 113111335313399, 1131113353133993, 113111335313399321, 11311133531339932153, 1131113353133993215379, 113111335313399321537911

Offset: 0

Patrick De Geest, May 15 1999

Clark Kimberling, Table of n, a(n) for n = 0..498

Cf. A048549-A048556, A261199-A261201, A261269-A261270.

f:= proc(n)
  local p, d;
  for d from 1 do
    p:= nextprime(n*10^d);
    if p < (n+1)*10^d then return p fi
  od
end proc:
A[1]:= 11:
for n from 2 to 20 do A[n]:= f(A[n-1]) od:
seq(A[n], n=1..20); # Robert Israel, Aug 16 2015

a = {11}; Do[k = 1; w = IntegerDigits[a[[n - 1]]];
While[CompositeQ@ FromDigits[Join[w, IntegerDigits@ k]], k += 2];
AppendTo[a, FromDigits[Join[w, IntegerDigits@ k]]], {n, 2, 15}]; a (* Michael De Vlieger, Sep 21 2015 *)

A048556 p(n+1) is next smallest prime beginning with p(n), initial prime is 19.

Original entry on oeis.org

19, 191, 1913, 19139, 1913903, 19139039, 191390393, 19139039303, 1913903930321, 191390393032123, 1913903930321233, 191390393032123361, 19139039303212336171, 1913903930321233617139, 191390393032123361713943

Offset: 0

Patrick De Geest, May 15 1999

Cf. A048549-A048555.

A048552 a(n+1) is next smallest prime beginning with a(n), initial prime is a(0) = 7.

Original entry on oeis.org

7, 71, 719, 7193, 71933, 719333, 71933317, 719333177, 71933317711, 7193331771103, 71933317711039, 7193331771103939, 719333177110393913, 7193331771103939133, 719333177110393913323, 71933317711039391332309, 719333177110393913323097, 719333177110393913323097047

Offset: 0

Patrick De Geest, May 15 1999

Robert Israel, Table of n, a(n) for n = 0..250

Cf. A048549, A048550, A048551, A048552, A048553, A048554, A048555, A048556.

f:= proc(n) option remember; local q,d,v;
    q:=procname(n-1);
    for d from 1 do
      v:= nextprime(q*10^d);
      if v < (q+1)*10^d then return v fi
    od
end proc:
f(0):= 7:
map(f, [$0..20]); # Robert Israel, Jan 26 2020

Nest[Function[{a, n}, Append[#, Catch@ Do[Do[If[PrimeQ@ #, Throw@ #; Break[], #] &@ FromDigits[n~Join~PadLeft[IntegerDigits[(5 j - 4 + Mod[3 j + 2, 4])/2], i]], {j, 4*10^(i - 1)}], {i, Infinity}]]] @@ {#, IntegerDigits[#[[-1]] ]} &, {7}, 17] (* Michael De Vlieger, Jan 26 2020 *)

next_A048552(p)=for(i=1,oo,my(q=nextprime(p*=10));q-p>10^i||return(q))
A048552(n,p=7)=vector(n,i,i>1&&p=next_A048552(p);p) \\ M. F. Hasler, Jan 26 2020

A048550 a(n+1) is the next smallest prime beginning with a(n), initial prime is 3.

Original entry on oeis.org

3, 31, 311, 3119, 31193, 3119309, 31193093, 311930933, 31193093317, 311930933179, 3119309331797, 311930933179703, 31193093317970371, 3119309331797037107, 311930933179703710759, 31193093317970371075907

Offset: 0

Patrick De Geest, May 15 1999

Robert Israel, Table of n, a(n) for n = 0..328

Cf. A048549, A048551, A048552, A048553, A048554, A048555, A048556.

f:= proc(n) local d,a;
  for d from 1 do
    for a from 10^d*n+1 by 2 to 10^d*(n+1) do
      if isprime(a) then return a fi
  od od
end proc:
R:= 3: x:= 3:
for i from 2 to 30 do
  x:= f(x);
  R:= R, x;
od:
R; # Robert Israel, Dec 13 2023

A048555 p(n+1) is next smallest prime beginning with p(n), initial prime is 17.

Original entry on oeis.org

17, 173, 1733, 17333, 1733309, 173330917, 1733309173, 17333091733, 1733309173319, 173330917331917, 17333091733191701, 1733309173319170103, 173330917331917010357, 17333091733191701035703

Offset: 0

Patrick De Geest, May 15 1999

Cf. A048549-A048556.

A055011 a(n+1) = next smallest prime beginning with a(n) when written in binary, starting with 2.

Original entry on oeis.org

2, 5, 11, 23, 47, 191, 383, 3067, 12269, 196307, 6281839, 50254717, 201018869, 804075479, 1608150959, 102921661397, 1646746582367, 13173972658937, 105391781271503, 210783562543007, 3372537000688127, 26980296005505019, 863369472176160611, 6906955777409284889

Offset: 0

Henry Bottomley, May 31 2000

a(5)=191 because a(4)=47 which in binary is 101111, none of 1011110(94) 1011111(95) 10111100(188) 10111101(189) 10111110 (190) are prime, but 10111111(191) is.

Cf. A048549 for base 10 analog.

A055011, A261200 and A261201 are all essentially the same sequence.

a055011 n = a055011_list !! n
a055011_list = iterate a208241 2  -- Reinhard Zumkeller, Feb 14 2013

A055011 := proc(n)
    option remember;
    if n = 0 then
        2 ;
    else
        A208241(procname(n-1)) ;
    end if;
end proc: # R. J. Mathar, May 06 2017

a(n+1) = A208241(a(n)). - Reinhard Zumkeller, Feb 14 2013

A048551 p(n+1) is next smallest prime beginning with p(n), initial prime is 5.

Original entry on oeis.org

5, 53, 5303, 530303, 53030317, 530303173, 53030317313, 530303173133, 53030317313327, 53030317313327047, 5303031731332704703, 530303173133270470327, 5303031731332704703273, 530303173133270470327321

Offset: 0

Patrick De Geest, May 15 1999

Cf. A048549-A048556.

A048554 p(n+1) is next smallest prime beginning with p(n), initial prime is 13.

Original entry on oeis.org

13, 131, 1319, 131909, 13190909, 1319090933, 131909093341, 13190909334101, 1319090933410141, 131909093341014131, 13190909334101413129, 131909093341014131297, 13190909334101413129739

Offset: 0

Patrick De Geest, May 15 1999

Cf. A048549-A048556.

A051670 Smallest prime that concatenated with all previous terms of sequence forms a prime.

Original entry on oeis.org

2, 3, 3, 3, 3, 23, 7, 3, 53, 19, 149, 571, 3, 131, 3, 151, 389, 31, 389, 97, 59, 277, 491, 181, 59, 67, 647, 1117, 797, 433, 41, 367, 29, 487, 719, 283, 347, 97, 1103, 193, 821, 13, 29, 31, 947, 619, 167, 229, 479, 271, 1217, 79, 2777, 241, 1361, 751, 83, 4603, 317

Offset: 1

Felice Russo, Dec 15 1999

			The 6th term of the sequence is 23 because that is smallest prime that when concatenated with previous terms 2, 3, 3, 3, 3, produces a prime (2333323).

A. Murthy, Smar. Notions J. Vol. 11, N. 1-2-3 Spring 2000

Paul Zimmermann, Table of n, a(n) for n = 1..1127 [First 200 terms from T. D. Noe]

Cf. A048549 and A083758.

nxt[{lst_,n_}]:=Module[{id=IntegerDigits[lst],np=2},While[ !PrimeQ[ FromDigits[ Join[id, IntegerDigits[np]]]],np=NextPrime[np]];{FromDigits[ Join[id,IntegerDigits[np]]],np}]; Transpose[NestList[nxt,{2,2},60]] [[2]] (* Harvey P. Dale, May 25 2015 *)
nxt[{l_,a_}]:=Module[{k=2},While[CompositeQ[l*10^IntegerLength[k]+ k],k= NextPrime[ k]];{l*10^IntegerLength[k]+k,k}]; NestList[nxt,{2,2},60][[All,2]] (* Harvey P. Dale, Aug 09 2020 *)

Extended by T. D. Noe, May 01 2010

A100893 a(n) = smallest n-digit prime formed by appending a digit to a(n-1); a(1) = 2.

Original entry on oeis.org

2, 23, 233, 2333, 23333

Offset: 1

Jorge Coveiro, Jan 10 2005

This sequence is finite because there is no prime a(6) since 233331,233333,233337,233339 are not prime.

This is an initial subsequence of A048549, A065122, A088603, and A127889; and for any b, the base b analog of this sequence is an initial subsequence of the base b analog of each of these three sequences. [From Franklin T. Adams-Watters, Jun 27 2009]

			a(1)=2
a(2)=23
a(3)=233
a(4)=2333
a(5)=23333

cp's OEIS Frontend

A048553 a(n+1) is next smallest prime beginning with a(n), initial prime is 11.

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A048556 p(n+1) is next smallest prime beginning with p(n), initial prime is 19.

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A048552 a(n+1) is next smallest prime beginning with a(n), initial prime is a(0) = 7.

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A048550 a(n+1) is the next smallest prime beginning with a(n), initial prime is 3.

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A048555 p(n+1) is next smallest prime beginning with p(n), initial prime is 17.

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A055011 a(n+1) = next smallest prime beginning with a(n) when written in binary, starting with 2.

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A048551 p(n+1) is next smallest prime beginning with p(n), initial prime is 5.

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A048554 p(n+1) is next smallest prime beginning with p(n), initial prime is 13.

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A051670 Smallest prime that concatenated with all previous terms of sequence forms a prime.

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A100893 a(n) = smallest n-digit prime formed by appending a digit to a(n-1); a(1) = 2.

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