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

A033679 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, 3, 3, 3, 21, 53, 69, 81, 139, 143, 223, 233, 261, 261, 399, 553, 609, 659, 673, 1017, 1187, 1357, 1571, 1641, 1839, 2151, 2191, 2499, 2511, 2607, 2667, 2681, 3081, 3351, 4291, 4319, 4353, 4489, 4733, 4819, 6003, 6011, 6631, 6797, 7113, 7429, 7547, 7651
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A069603, A074338, A033680, A033681, A046254, A046255, A046256, A046257, A046258, A046259, A111524.

Programs

  • Maple
    R:= 2,3: p:= 23: x:= 3:
for count from 3 to 100 do
  for y from x by 2 do
    if isprime(10^(1+ilog10(y))*p+y) then
      R:= R, y; p:= 10^(1+ilog10(y))*p+y; x:= y;
      break
    fi
od od:
R; # Robert Israel, Nov 22 2020
  • Mathematica
    a[1] = 2; 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 *)

Extensions

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

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 *)

A048549 a(n+1) is next smallest prime beginning with a(n), initial prime is 2.

Original entry on oeis.org

2, 23, 233, 2333, 23333, 2333321, 233332117, 2333321173, 233332117313, 23333211731399, 2333321173139903, 2333321173139903173, 23333211731399031733, 2333321173139903173301, 2333321173139903173301021
Offset: 1

Views

Author

Patrick De Geest, May 15 1999

Keywords

Links

Crossrefs

Cf. A048550, A048551, A048552, A048553, A048554, A048555, A048556, A030456.
Similar to but different from A069603.

Programs

  • Mathematica
    b = 10; s = {{2}};
Do[NestWhile[# + 1 &, 0, ! (PrimeQ[FromDigits[tmp = Join[Last[s], (nn = #;
IntegerDigits[nn - Sum[b^n, {n, l = NestWhile[# + 1 &, 1, ! (nn - (Sum[b^n, {n, #}]) < 0) &] - 1}], b, l + 1])], b]]) &]; AppendTo[s, tmp], {20}]; Map[FromDigits, s] (* Peter J. C. Moses, Aug 06 2015 *)
Showing 1-10 of 14 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.