A033680 -id:A033680 - cp's OEIS frontend

A074336 a(1) = 1; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

1, 3, 7, 11, 13, 29, 37, 113, 121, 149, 151, 201, 219, 251, 451, 453, 573, 669, 689, 697, 749, 913, 969, 1157, 1269, 1503, 1531, 1809, 2087, 2163, 2179, 2511, 2537, 2599, 2709, 2789, 2929, 3243, 3989, 4033, 4151, 5019, 5389, 5423, 5599, 6179, 6433, 8267

Offset: 1

Zak Seidov, Sep 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 1..200 (first 100 terms from Paolo P. Lava)

Cf. A033680, A092528, A069602, A074338, A074339, A074340, A074341, A074342, A074343, A074344, A074345, A074346.

a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 1 + Mod[a[n - 1], 2], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 48}] (* Robert G. Wilson v *)
nxt[{j_,a_}]:=Module[{k=a+1},While[!PrimeQ[j*10^IntegerLength[k]+k],k++];{j*10^ IntegerLength[ k]+k,k}]; NestList[nxt,{1,1},50][[;;,2]] (* Harvey P. Dale, Sep 10 2024 *)

More terms from Robert G. Wilson v, Aug 05 2005

A033679 a(1) = 2; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

2, 3, 3, 3, 3, 21, 53, 69, 81, 139, 143, 223, 233, 261, 261, 399, 553, 609, 659, 673, 1017, 1187, 1357, 1571, 1641, 1839, 2151, 2191, 2499, 2511, 2607, 2667, 2681, 3081, 3351, 4291, 4319, 4353, 4489, 4733, 4819, 6003, 6011, 6631, 6797, 7113, 7429, 7547, 7651

Offset: 1

N. J. A. Sloane

Robert Israel, Table of n, a(n) for n = 1..300

Cf. A069603, A074338, A033680, A033681, A046254, A046255, A046256, A046257, A046258, A046259, A111524.

R:= 2,3: p:= 23: x:= 3:
for count from 3 to 100 do
  for y from x by 2 do
    if isprime(10^(1+ilog10(y))*p+y) then
      R:= R, y; p:= 10^(1+ilog10(y))*p+y; x:= y;
      break
    fi
od od:
R; # Robert Israel, Nov 22 2020

a[1] = 2; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k ++ ]; k]; Table[ a[n], {n, 47}] (* Robert G. Wilson v, Aug 05 2005 *)

More terms from Patrick De Geest, May 15 1998

More terms from Robert G. Wilson v, Aug 05 2005

A092528 a(1) = 1; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

1, 1, 3, 11, 1, 3, 3, 53, 13, 39, 9, 3, 21, 53, 79, 11, 19, 59, 27, 49, 21, 23, 211, 153, 189, 3, 161, 121, 167, 183, 193, 77, 21, 349, 107, 129, 343, 119, 241, 143, 37, 77, 31, 159, 183, 531, 1517, 7, 59, 159, 123, 9, 1513, 203, 343, 59, 9, 999, 813, 421, 209, 517, 3

Offset: 1

Christer Mauritz Blomqvist (MauritzTortoise(AT)hotmail.com), Apr 08 2004

			The first few terms are 1,1,3,11,1,3,3,53,13,39,9,3. The next integer you can concatenate to the end of this to get a prime is 21 so the next term is 21. If you require terms to have all digits odd you would get 399 instead, giving A069604.

Cf. A033680, A074336, A069602, A069604, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

nn[a_] := For[b = 1, ! PrimeQ[n], b = b + 1, n = a*10^Floor[Log[10, b] + 1]] (* o get the next number in the sequence if a is the concatenation of all previous. *) nnt[m_] := (t = 1; Table[c = nnn[t]; t = c[[2]]; c[[1]], {m}]) (* To get a table of the first n terms, ignoring a(1)=1*)
a[1] = 1; a[n_] := a[n] = Block[{k = 1, c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 63}] (* Robert G. Wilson v, Aug 05 2005 *)

A033681 a(1) = 3; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

3, 7, 9, 51, 51, 51, 97, 131, 157, 159, 243, 309, 327, 363, 383, 411, 487, 639, 873, 983, 1231, 1257, 1337, 1549, 1589, 2101, 2159, 2317, 2871, 2907, 4053, 4097, 4597, 4703, 5559, 5799, 6337, 6527, 6561, 6939, 7147, 7167, 7839, 8403, 8873, 9237, 9541, 9771

Offset: 1

N. J. A. Sloane

nonn

Cf. A069605, A074339, A033680, A033679, A046254, A046255, A046256, A046257, A046258, A046259, A111524.

a[1] = 3; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 48}] (* Robert G. Wilson v *)

More terms from Patrick De Geest, May 15 1998

More terms from Robert G. Wilson v, Aug 05 2005

A046254 a(1) = 4; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

4, 7, 9, 9, 39, 47, 57, 81, 111, 123, 243, 283, 287, 313, 407, 507, 807, 1057, 1209, 1211, 1443, 1447, 1619, 2019, 2269, 2429, 2637, 2679, 2751, 3007, 3287, 3789, 3829, 3833, 3949, 4151, 4533, 4821, 5097, 5331, 5457, 5529, 5691, 6021, 6153, 6393, 6409

Offset: 1

Patrick De Geest, May 15 1998

nonn

Cf. A069606, A074340, A033680, A033679, A033681, A046255, A046256, A046257, A046258, A046259, A111524.

a[1] = 4; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k ++ ]; k]; Table[ a[n], {n, 47}] (* Robert G. Wilson v, Aug 05 2005 *)

A046256 a(1) = 6; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

6, 7, 7, 9, 27, 59, 69, 181, 201, 257, 267, 399, 573, 603, 861, 901, 923, 1021, 1133, 1239, 1251, 1519, 1589, 1729, 1863, 1901, 2541, 3001, 3017, 3049, 3243, 4407, 4481, 5457, 5839, 5889, 5919, 6159, 6201, 6293, 6577, 6603, 6969, 7217, 8131, 8981, 9033

Offset: 1

Patrick De Geest, May 15 1998

Michael S. Branicky, Table of n, a(n) for n = 1..441 (terms 1..100 from Harvey P. Dale)

Cf. A069608, A074342, A033680, A033679, A033681, A046254, A046255, A046257, A046258, A046259, A111524.

a[1] = 6; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k ++ ]; k]; Table[ a[n], {n, 47}] (* Robert G. Wilson v, Aug 05 2005 *)
nxt[{j_,a_}]:=Module[{k=a},While[!PrimeQ[j*10^IntegerLength[k]+k], k++];{j*10^IntegerLength[k]+k,k}]; Transpose[NestList[nxt,{6,6},50]][[2]] (* Harvey P. Dale, May 07 2016 *)

from sympy import isprime
def aupton(terms):
  alst, astr = [6], "6"
  for n in range(2, terms+1):
    an = alst[-1]
    while not isprime(int(astr+str(an))): an += 1
    alst, astr = alst + [an], astr + str(an)
  return alst
print(aupton(62)) # Michael S. Branicky, Jun 07 2021

A046257 a(1) = 7; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

7, 9, 19, 27, 47, 57, 61, 81, 179, 211, 251, 273, 373, 477, 581, 753, 847, 909, 909, 939, 957, 1173, 1311, 1343, 1543, 1619, 1693, 1739, 1879, 1971, 2141, 2523, 2653, 2729, 2863, 3201, 3293, 3411, 3621, 3753, 5023, 5421, 5459, 5481, 6403, 6827, 7041, 7669

Offset: 1

Patrick De Geest, May 15 1998

nonn

All terms must be odd. - Harvey P. Dale, Oct 21 2023

Robert Israel, Table of n, a(n) for n = 1..512

Cf. A069609, A074343, A033680, A033679, A033681, A046254, A046255, A046256, A046258, A046259, A111524.

A:= 7: x:= 7: count:= 1:
for i from 7 by 2 while count < 10000 do
 while isprime(x*10^(1+ilog10(i))+i) do
   x:= x*10^(1+ilog10(i))+i; A:= A,i; count:= count+1;
od od:
A; # Robert Israel, Jan 21 2024

a[1] = 7; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 46}] (* Robert G. Wilson v, Aug 05 2005 *)
nxt[{j_,a_}]:=Module[{k=a},While[CompositeQ[j*10^IntegerLength[k]+k],k+=2];{j*10^IntegerLength[k]+k,k}]; NestList[nxt,{7,7},50][[;;,2]] (* Harvey P. Dale, Oct 21 2023 *)

A046258 a(1) = 8; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

8, 9, 23, 51, 69, 81, 93, 129, 169, 179, 181, 273, 321, 321, 449, 639, 769, 857, 1047, 1213, 1233, 1443, 1587, 1637, 1953, 2433, 2599, 2639, 2901, 3261, 3681, 4059, 5109, 5169, 5407, 5691, 6149, 6531, 7939, 8081, 8211, 8439, 8589, 8623, 8663, 8757, 9459

Offset: 1

Patrick De Geest, May 15 1998

Robert Israel, Table of n, a(n) for n = 1..400

Cf. A069610, A074344, A033680, A033679, A033681, A046254, A046255, A046256, A046257, A046259, A111524.

A[1]:= 8: A[2]:= 9: x:= 89:
for n from 3 to 100 do
  for y from A[n-1] by 2 do
    z:= x*10^(1+ilog10(y))+y;
    if isprime(z) then break fi;
  od:
  A[n]:= y;
  x:= z;
od:
seq(A[i],i=1..100); # Robert Israel, May 30 2018

a[1] = 8; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k ++ ]; k]; Table[ a[n], {n, 47}] (* Robert G. Wilson v, Aug 05 2005 *)
nxt[{jp_,a_}]:=Module[{k=a},While[CompositeQ[jp 10^IntegerLength[k]+k],k++];{jp 10^IntegerLength[k]+ k,k}]; NestList[nxt,{8,8},50][[;;,2]] (* Harvey P. Dale, Apr 10 2024 *)

A074341 a(1) = 4; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

4, 7, 9, 11, 81, 87, 109, 117, 123, 129, 201, 389, 429, 441, 771, 811, 831, 1037, 1143, 1299, 1569, 1581, 1803, 1837, 1943, 2053, 2171, 2379, 2431, 3201, 3437, 3489, 3723, 3841, 4289, 4801, 5523, 6249, 7083, 7467, 7749, 8171, 9073, 9333, 9683, 9781, 10833

Offset: 1

Zak Seidov, Sep 23 2002

Harvey P. Dale, Table of n, a(n) for n = 1..100

Cf. A033679, A033680, A033681.

Cf. A069606, A046254, A074336, A074338, A074339, A074340, A074342, A074343, A074344, A074345, A074346.

a[1] = 4; a[n_] := a[n] = Block[{k = a[n - 1] + 1 + Mod[a[n - 1], 2], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 47}] (* Robert G. Wilson v *)
nxt[{j_,a_}]:=Module[{k=a+1},While[!PrimeQ[j*10^IntegerLength[k]+k],k++];{j*10^IntegerLength[k]+k,k}]; NestList[nxt,{4,4},50][[;;,2]] (* Harvey P. Dale, Apr 07 2025 *)

More terms from Robert G. Wilson v, Aug 05 2005

A111524 a(1) = 10; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

10, 13, 23, 49, 111, 113, 171, 211, 293, 309, 309, 469, 639, 759, 951, 1037, 1057, 1083, 1257, 1269, 1287, 1341, 1551, 1637, 1677, 1981, 1989, 2021, 2059, 2357, 2583, 2697, 2967, 3289, 6789, 7073, 7323, 7369, 7463, 7501, 7709, 7869, 8029, 8069, 8077, 8519

Offset: 1

Patrick De Geest, Zak Seidov and Robert G. Wilson v, Aug 05 2005

Michael S. Branicky, Table of n, a(n) for n = 1..449

Cf. A111525, A074346, A033680, A033679, A033681.

Cf. A046254, A046255, A046256, A046257, A046258, A046259.

a[1] = 10; a[n_] := a[n] = Block[{k = a[n - 1] + 1 + Mod[a[n - 1], 2], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 46}] (* Robert G. Wilson v, Aug 05 2005 *)

from sympy import isprime
def aupton(terms):
    alst, astr = [10], "10"
    while len(alst) < terms:
        k = alst[-1] + (1 - alst[-1]%2)
        while not isprime(int(astr+str(k))): k += 2
        alst.append(k)
        astr += str(k)
    return alst
print(aupton(46)) # Michael S. Branicky, Oct 13 2021

cp's OEIS Frontend

A074336 a(1) = 1; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A033679 a(1) = 2; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A092528 a(1) = 1; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A033681 a(1) = 3; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A046254 a(1) = 4; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A046256 a(1) = 6; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A046257 a(1) = 7; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A046258 a(1) = 8; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A074341 a(1) = 4; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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