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 14 results. Next

A069606 a(1) = 4; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

4, 1, 9, 11, 19, 3, 3, 41, 51, 51, 87, 19, 63, 23, 13, 29, 3, 219, 183, 27, 27, 3, 3, 27, 217, 129, 381, 59, 163, 281, 169, 57, 77, 31, 9, 9, 243, 147, 21, 239, 39, 219, 693, 37, 143, 789, 9, 163, 219, 497, 51, 301, 149, 103, 117, 309, 591, 159, 741, 131, 541, 1377, 207
Offset: 1

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

			a(5) = 19 and the number 4191119 is a prime.

Crossrefs

Cf. A069602, A069604, A046254, A074340, A092528, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    a[1] = 4; 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 *)
nxt[{jxt_,a_}]:=Module[{n=1},While[CompositeQ[jxt*10^IntegerLength[n]+n],n++];{jxt*10^IntegerLength[ n]+n,n}]; NestList[nxt,{4,4},70][[;;,2]] (* Harvey P. Dale, Oct 06 2023 *)

Extensions

More terms from Jason Earls, Jun 13 2002

A069605 a(1) = 3; a(n) = smallest number such that the concatenation a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

3, 1, 1, 9, 3, 17, 1, 3, 9, 39, 33, 53, 1, 21, 27, 113, 99, 123, 3, 91, 39, 29, 141, 87, 67, 297, 87, 333, 59, 67, 509, 103, 279, 99, 141, 107, 9, 1, 123, 83, 529, 521, 517, 137, 249, 459, 543, 583, 513, 21, 53, 1029, 657, 219, 313, 17, 237, 19, 689, 339, 307, 23
Offset: 1

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

			a(6) = 17 and the number 3119317 is a prime.

Crossrefs

Cf. A033681, A074339, A092528, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    a[1] = 3; 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 *)

Extensions

More terms from Jason Earls, Jun 13 2002

A069608 a(1) = 6; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

6, 1, 3, 1, 41, 19, 17, 1, 81, 27, 89, 3, 79, 29, 1, 111, 29, 13, 119, 207, 21, 33, 19, 413, 49, 71, 183, 223, 153, 21, 261, 369, 29, 319, 107, 1, 273, 81, 711, 507, 87, 579, 401, 7, 33, 771, 477, 33, 371, 91, 1559, 357, 297, 9, 177, 523, 77, 103, 167, 199, 143, 199
Offset: 1

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

			a(5) = 41 and the number 613141 is a prime.

Links

Crossrefs

Cf. A069602, A069604, A046256, A074342, A092528, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    a[1] = 6; 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 = [6], "6"
  for n in range(2, terms+1):
    an = 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 01 2021

Extensions

More terms from Jason Earls, Jun 13 2002

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

A069611 a(1) = 9; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

9, 7, 1, 9, 17, 13, 33, 23, 7, 77, 31, 59, 51, 27, 7, 269, 439, 11, 429, 163, 39, 11, 463, 77, 63, 39, 33, 93, 21, 139, 53, 159, 49, 9, 291, 111, 21, 23, 349, 83, 3, 37, 11, 57, 21, 219, 507, 1233, 429, 147, 627, 127, 399, 27, 63, 423, 111, 633, 1391, 297, 831, 283
Offset: 1

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

			a(5) = 17 and the number 971917 is a prime.

Crossrefs

Cf. A069602, A069604, A046259, A074345, A092528, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    a[1] = 9; 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 *)

Extensions

More terms from Jason Earls, Jun 13 2002

A069607 a(1) = 5; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

5, 3, 23, 1, 3, 9, 21, 9, 21, 23, 43, 3, 23, 7, 21, 89, 37, 21, 137, 1, 119, 493, 143, 133, 483, 267, 179, 7, 333, 359, 439, 101, 33, 31, 533, 19, 63, 39, 333, 839, 63, 693, 423, 327, 73, 29, 39, 21, 517, 27, 99, 251, 7, 411, 243, 33, 149, 49, 227, 283, 303, 351, 303
Offset: 1

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

			a(5) = 3 and the number 532313 is a prime.

Links

Crossrefs

Cf. A069602, A069604, A046255, A074341, A092528, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    a[1] = 5; 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):
  astr, alst = '5', [5]
  for n in range(2, terms+1):
    an = 1
    while not isprime(int(astr + str(an))): an += 1
    astr, alst = astr + str(an), alst + [an]
  return alst
print(aupton(63)) # Michael S. Branicky, May 03 2021

Extensions

More terms from Jason Earls, Jun 13 2002

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

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.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

Extensions

More terms from Patrick De Geest, May 15 1998
More terms from Robert G. Wilson v, Aug 05 2005

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

A069603 a(1) = 2; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

2, 3, 3, 3, 3, 21, 17, 3, 13, 99, 17, 3, 7, 77, 19, 119, 7, 33, 29, 49, 149, 43, 23, 99, 9, 31, 57, 93, 29, 21, 91, 59, 31, 39, 87, 11, 121, 231, 279, 269, 51, 21, 313, 297, 527, 309, 27, 21, 67, 63, 431, 231, 13, 99, 407, 453, 69, 409, 189, 11, 31, 21, 23, 19, 93, 1143
Offset: 1

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

			a(6) = 21 and the number 2333321 is a prime.

Links

Crossrefs

Cf. A033679, A074338, A092528, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    a[1] = 2; 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 *)
  • Python
    from gmpy2 import is_prime
from itertools import count, islice
def agen(): # generator of terms
    an, s = 2, "2"
    while True:
        yield an
        an = next(k for k in count(3, 2) if is_prime(int(s+str(k))))
        s += str(an)
print(list(islice(agen(), 66))) # Michael S. Branicky, May 11 2023

Extensions

More terms from Jason Earls, Jun 13 2002
Showing 1-10 of 14 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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