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 1-10 of 11 results. Next

A069609 a(1) = 7; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

7, 1, 9, 3, 3, 3, 17, 7, 11, 37, 11, 9, 31, 9, 17, 13, 93, 3, 167, 67, 119, 93, 31, 33, 143, 99, 297, 91, 69, 83, 1, 33, 23, 27, 199, 333, 123, 549, 17, 67, 141, 33, 39, 167, 21, 217, 279, 419, 69, 517, 71, 451, 171, 39, 191, 93, 43, 11, 303, 777, 33, 67, 207, 369, 489
Offset: 1

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

			a(7) = 17 and the number 71933317 is a prime.

Links

Crossrefs

Cf. A069602, A069604, A046257, A074343, A092528, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    a[1] = 7; 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, 67}] (* Robert G. Wilson v, Aug 05 2005 *)
nxt[{j_,a_}]:=Module[{k=1},While[CompositeQ[j*10^IntegerLength[k]+k],k++];{j*10^IntegerLength[k]+k,k}]; NestList[nxt,{7,7},70][[All,2]] (* Harvey P. Dale, May 06 2022 *)

Extensions

More terms from Jason Earls, Jun 13 2002

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.

Original entry on oeis.org

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

Views

Author

Zak Seidov, Sep 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

Extensions

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

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

Views

Author

Patrick De Geest, May 15 1998

Keywords

Comments

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

Links

Crossrefs

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

Programs

  • Maple
    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
  • Mathematica
    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 *)

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

Views

Author

Zak Seidov, Sep 23 2002

Keywords

Crossrefs

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

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

Zak Seidov, Sep 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • Python
    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

Extensions

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

Views

Author

Zak Seidov, Sep 23 2002

Keywords

Links

Crossrefs

Cf. A033679, A033680, A033681.
Cf. A069606, A046254, A074336, A074338, A074339, A074340, A074342, A074343, A074344, A074345, A074346.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

Zak Seidov, Sep 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • Python
    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

Extensions

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

Views

Author

Zak Seidov, Sep 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

Zak Seidov, Sep 23 2002

Keywords

Links

Crossrefs

Cf. A111524, A111525, A074336.
Cf. A074338, A074339, A074340, A074341, A074342, A074343, A074344, A074345.

Programs

  • Mathematica
    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 *)
  • Python
    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

Extensions

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

Views

Author

Zak Seidov, Sep 23 2002

Keywords

Crossrefs

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

Programs

  • Mathematica
    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 *)

Extensions

More terms from Robert G. Wilson v, Aug 05 2005
Showing 1-10 of 11 results. Next

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