A074336 -id:A074336 - cp's OEIS frontend

A033680 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, 1, 3, 11, 13, 29, 39, 49, 83, 141, 247, 273, 291, 347, 373, 401, 441, 567, 571, 651, 903, 957, 1001, 1129, 1401, 1457, 1467, 1561, 1889, 2083, 2169, 2523, 2717, 2743, 3447, 3509, 3711, 4087, 4899, 4983, 5087, 5151, 5263, 5429, 5551, 6017, 7389, 7839

Offset: 1

N. J. A. Sloane

Giovanni Resta, Table of n, a(n) for n = 1..800

Cf. A074336, A092528, A069602, A033679, A033681, A046254, A046255, A046256, A046257, A046258, A046259, A111524.

a[1] = 1; 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 *)
nxt[{c_,a_}]:=Module[{x=a},While[!PrimeQ[FromDigits[Join[c,IntegerDigits[ x]]]],x+=2];{Join[c,IntegerDigits[x]],x}]; NestList[nxt,{{1},1},50][[All,2]] (* Harvey P. Dale, Sep 14 2018 *)

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 *)

A074338 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, 9, 11, 13, 63, 71, 93, 187, 189, 201, 207, 243, 347, 369, 439, 473, 529, 611, 847, 1209, 1331, 1423, 1581, 1593, 1617, 1679, 1791, 2067, 2529, 2541, 2563, 2751, 3347, 3583, 3677, 3777, 4359, 4701, 4771, 5657, 6183, 6193, 6353, 6511, 6539, 6769, 6939

Offset: 1

Zak Seidov, Sep 23 2002

Cf. A033679, A069603, A074336, A074339, A074340, A074341, A074342, A074343, A074344, A074345, A074346.

a[1] = 2; 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 *)

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

A074340 a(1) = 5; 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

5, 9, 23, 37, 39, 47, 57, 97, 119, 187, 257, 271, 273, 281, 309, 367, 449, 529, 687, 759, 933, 1031, 1131, 1237, 1263, 1343, 1731, 1861, 2177, 2337, 2589, 2607, 2743, 3191, 3199, 3281, 3499, 3807, 3867, 4133, 6079, 6189, 6593, 7207, 7479, 7523, 8569, 8571

Offset: 1

Zak Seidov, Sep 23 2002

Michael S. Branicky, Table of n, a(n) for n = 1..411

Cf. A069606, A046254, A074336, A074338, A074339, A074341, A074342, A074343, A074344, A074345, A074346.

a[1] = 5; 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 *)

from sympy import isprime
def aupton(terms):
  alst, astr = [5], "5"
  while len(alst) < terms:
    an = alst[-1] + 2
    while an%5 ==0 or not isprime(int(astr + str(an))): an += 2
    alst, astr = alst + [an], astr + str(an)
  return alst
print(aupton(48)) # Michael S. Branicky, May 09 2021

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

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

A074342 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, 19, 21, 23, 27, 57, 183, 207, 231, 247, 267, 399, 417, 441, 459, 569, 603, 693, 847, 933, 1107, 1149, 1197, 1251, 1581, 1619, 2061, 2137, 2139, 2339, 2643, 2703, 2743, 2847, 2987, 3199, 3447, 3477, 3641, 3919, 4241, 4369, 4599, 4761, 6647, 6739, 6831

Offset: 1

Zak Seidov, Sep 23 2002

Michael S. Branicky, Table of n, a(n) for n = 1..439

Cf. A046256, A069608, A074336, A074338, A074339, A074340, A074341, A074343, A074344, A074345, A074346.

a[1] = 6; 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+2},While[CompositeQ[j(10^ IntegerLength[ k])+k],k+=2];{j(10^IntegerLength[k])+k,k}]; Join[{6},NestList[ nxt,{67,7},50][[All,2]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 19 2021 *)

from sympy import isprime
def aupton(terms):
  alst, astr = [6], "6"
  for n in range(2, terms+1):
    an = alst[-1] + 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

Corrected and extended by Robert G. Wilson v, Aug 05 2005

A074345 a(1) = 9; 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

9, 11, 21, 33, 39, 71, 73, 81, 101, 123, 193, 257, 271, 293, 379, 387, 407, 627, 669, 931, 1073, 1179, 1273, 1481, 2587, 2627, 2923, 3063, 3617, 3931, 4073, 4093, 4199, 4491, 4801, 5387, 5647, 5739, 5859, 5979, 6149, 6369, 7527, 8053, 8207, 8647, 8949, 8981

Offset: 1

Zak Seidov, Sep 23 2002

Harvey P. Dale, Table of n, a(n) for n = 1..200

Cf. A046259, A069611, A074336, A074338, A074339, A074340, A074341, A074342, A074343, A074344, A074346.

a[1] = 9; 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[{c=a+2},While[CompositeQ[j*10^IntegerLength[c]+c],c+=2];{j*10^IntegerLength[c]+c,c}]; NestList[nxt,{9,9},50][[All,2]] (* Harvey P. Dale, Jan 26 2022 *)

Corrected and extended by Robert G. Wilson v, Aug 05 2005

A074346 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, 333, 387, 463, 479, 513, 687, 933, 973, 993, 1329, 1433, 1449, 1551, 2071, 2271, 2423, 2587, 2621, 2659, 2757, 2771, 2911, 3081, 3243, 3279, 3671, 4243, 4247, 4371, 4453, 4511, 5229, 6097, 6177, 6293, 6571

Offset: 1

Zak Seidov, Sep 23 2002

Michael S. Branicky, Table of n, a(n) for n = 1..439

Cf. A111524, A111525, A074336.

Cf. A074338, A074339, A074340, A074341, A074342, A074343, A074344, A074345.

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

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

A074339 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, 57, 103, 119, 121, 183, 293, 301, 351, 447, 479, 577, 741, 839, 1051, 1277, 1431, 1633, 1877, 2043, 2251, 2303, 2659, 2937, 3447, 3897, 3969, 4059, 4179, 4371, 4389, 4563, 4841, 4903, 5097, 5103, 5369, 5689, 6621, 6831, 6927, 7479, 9227, 9351

Offset: 1

Zak Seidov, Sep 23 2002

Cf. A069605, A033681, A074336, A074338, A074340, A074341, A074342, A074343, A074344, A074345, A074346.

a[1] = 3; 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 *)

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

A074343 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, 971, 1399, 1623, 1967, 2139, 2629, 2979, 3297, 3393, 3647, 3793, 4281, 4337, 4411, 4517, 4831, 4979, 5131, 5841, 5897, 5953, 5991, 6287, 6309, 8101, 8147, 8521, 8877, 8969, 9699

Offset: 1

Zak Seidov, Sep 23 2002

Cf. A046257, A069609, A074336, A074338, A074339, A074340, A074341, A074342, A074344, A074345, A074346.

a[1] = 7; 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 *)

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

cp's OEIS Frontend

A033680 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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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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A074338 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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A074340 a(1) = 5; 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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A074342 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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A074345 a(1) = 9; 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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A074346 a(1) = 10; 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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A074339 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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