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

A069610 a(1) = 8; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

8, 3, 9, 11, 7, 21, 23, 3, 7, 29, 3, 99, 9, 93, 1, 39, 33, 21, 137, 123, 57, 13, 191, 3, 163, 9, 143, 63, 21, 157, 521, 163, 161, 43, 161, 109, 107, 121, 423, 57, 71, 7, 173, 469, 107, 57, 177, 411, 49, 149, 61, 291, 413, 271, 299, 693, 349, 149, 73, 299, 271, 521
Offset: 1

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

			a(4) = 11 and the number 83911 is a prime.

Crossrefs

Cf. A046258, A074344, A092528, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    a[1] = 8; 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 *)
  • Python
    from sympy import isprime
def aupton(terms):
    alst, astr = [8], '8'
    for n in range(2, terms+1):
        an = 1
        while not isprime(int(astr + str(an))): an += 2
        alst, astr = alst + [an], astr + str(an)
    return alst
print(aupton(62)) # Michael S. Branicky, Aug 03 2021

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

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

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

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

Programs

  • Maple
    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
  • Mathematica
    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 *)

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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