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 20 results. Next

A236529 Primes arising in A069607.

Original entry on oeis.org

5, 53, 5323, 53231, 532313, 5323139, 532313921, 5323139219, 532313921921, 53231392192123, 5323139219212343, 53231392192123433, 5323139219212343323, 53231392192123433237, 5323139219212343323721, 532313921921234332372189, 53231392192123433237218937, 5323139219212343323721893721
Offset: 1

Views

Author

Derek Orr, Jan 27 2014

Keywords

Comments

a(n+1) is the next smallest prime beginning with a(n). Initial term is 5.

Examples

			a(1) = 5.
a(2) is the next smallest prime that begins with 5, so a(2) = 53.
a(3) is the next smallest prime that begins with 53, so a(3) = 5323.
...and so on.

Crossrefs

Cf. A069607, A110773, A048553.

Programs

  • Python
    import sympy
from sympy import isprime
def b(x):
  num = str(x)
  n = 1
  while n < 10**3:
    new_num = str(x) + str(n)
    if isprime(int(new_num)):
      print(int(new_num))
      x = new_num
      n = 1
    else:
      n += 1
b(5)

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

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

A069614 a(1) = 2; a(2n) = smallest prime starting (the most significant digits) with a(2n-1) (i.e., as a right concatenation of a(2n-1) and a number with no insignificant zeros); a(2n+1) = smallest prime ending in (the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.

Original entry on oeis.org

2, 23, 223, 2237, 32237, 3223729, 63223729, 632237297, 2632237297, 263223729721, 12263223729721, 1226322372972173, 171226322372972173, 17122632237297217381, 2117122632237297217381, 21171226322372972173813
Offset: 1

Views

Author

Amarnath Murthy, Mar 27 2002

Keywords

Examples

			a(4) = 2111 starting with a(3) = 211 and a(5) = 22111 ending in a(4) = 2111.

Crossrefs

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

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

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

Views

Author

Christer Mauritz Blomqvist (MauritzTortoise(AT)hotmail.com), Apr 08 2004

Keywords

Examples

			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.

Crossrefs

Cf. A033680, A074336, A069602, A069604, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

Programs

  • Mathematica
    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 *)
Showing 1-10 of 20 results. Next

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

Content is available under The OEIS End-User License Agreement.