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 13 results. Next

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

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

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

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

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

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

Patrick De Geest, May 15 1998

Keywords

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • Python
    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

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 *)

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

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

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

Views

Author

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

Keywords

Links

Crossrefs

Cf. A111525, A074346, A033680, A033679, A033681.
Cf. A046254, A046255, A046256, A046257, A046258, A046259.

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

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