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.

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A069618 a(1) = 6; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and 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

6, 61, 461, 46133, 246133, 2461337, 22461337, 224613371, 12224613371, 1222461337117, 151222461337117, 15122246133711733, 615122246133711733, 615122246133711733213, 9615122246133711733213, 961512224613371173321349
Offset: 1

Views

Author

Amarnath Murthy, Mar 27 2002

Keywords

Examples

			a(4) = 46133 starting with a(3) = 461 and a(5) = 246133 in a(4) = 46133.

Crossrefs

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613, A069614, A069615, A069616, A069617.

Extensions

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

A069619 a(1) = 7; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and 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

7, 71, 271, 2711, 52711, 5271121, 135271121, 1352711219, 271352711219, 27135271121911, 1227135271121911, 122713527112191161, 20122713527112191161, 20122713527112191161109, 2720122713527112191161109
Offset: 1

Views

Author

Amarnath Murthy, Mar 27 2002

Keywords

Examples

			a(4) = 2711 starting with a(3) = 271 and a(5) = 52711 in a(4) = 2711.

Crossrefs

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613, A069614, A069615, A069616, A069617, A069618.

Extensions

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

A329876 Lexicographically earliest sequence of positive integers such that for n > 1, the concatenation of a(n), a(n-1), ..., a(1), in decimal, is a prime number.

Original entry on oeis.org

1, 1, 2, 4, 3, 2, 4, 15, 3, 9, 20, 4, 3, 11, 31, 6, 24, 23, 82, 11, 21, 3, 22, 20, 63, 19, 56, 22, 17, 42, 105, 31, 2, 4, 27, 96, 42, 5, 72, 19, 20, 22, 32, 102, 31, 104, 4, 24, 95, 21, 13, 12, 9, 38, 3, 58, 38, 78, 31, 119, 31, 45, 107, 42, 12, 9, 21, 66, 181
Offset: 1

Views

Author

Rémy Sigrist, Nov 23 2019

Keywords

Comments

For any n > 0, the concatenation of a(n+1) and A053582(n) gives A053582(n+1).

Links

Crossrefs

See A053582 for the corresponding concatenations.

Programs

  • PARI
    print1 (v=1); for (n=2, 69, s=(b=10)^#digits(v,b); for (k=1, oo, if (isprime(v+=s), print1 (", "k); break)))

Formula

The first terms, alongside their concatenations, are:
n a(n) A053582(n)
-- ---- -----------
1 1 1
2 1 11
3 2 211
4 4 4211
5 3 34211
6 2 234211
7 4 4234211
8 15 154234211
9 3 3154234211
10 9 93154234211

A069620 a(1) = 8; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and 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

8, 83, 283, 2833, 32833, 328331, 2328331, 232833127, 3232833127, 323283312749, 14323283312749, 1432328331274927, 281432328331274927, 28143232833127492741, 3628143232833127492741, 36281432328331274927411
Offset: 1

Views

Author

Amarnath Murthy, Mar 27 2002

Keywords

Examples

			a(4) = 2833 starting with a(3) = 283 and a(5) = 32833 ending in a(4) = 2833.

Crossrefs

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613, A069614, A069615, A069616, A069617, A069618, A069619.

Extensions

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

A329875 a(1) = 1, for n > 0, a(n+1) is the least prime number > a(n) whose binary expansion ends with the binary expansion of a(n).

Original entry on oeis.org

1, 3, 7, 23, 151, 919, 8087, 90007, 2449303, 6643607, 115695511, 786784151, 2934267799, 183322894231, 1007956615063, 4306491498391, 101063514742679, 2634338305138583, 106217129734659991, 2267944950872498071, 69137392218069622679, 2504107609947730435991
Offset: 1

Views

Author

Rémy Sigrist, Nov 23 2019

Keywords

Comments

This sequence is a binary variant of A053582.
Dirichlet's theorem on arithmetic progressions guaranties that this sequence is infinite.
We can build a similar sequence for any base b > 1 and any starting value coprime to b.

Examples

			The first terms, alongside their binary representations, are:
  n  a(n)     bin(a(n))
  -  -------  ----------------------
  1        1                       1
  2        3                      11
  3        7                     111
  4       23                   10111
  5      151                10010111
  6      919              1110010111
  7     8087           1111110010111
  8    90007       10101111110010111
  9  2449303  1001010101111110010111

Crossrefs

Cf. A053582, A329877.

Programs

  • PARI
    print1 (v=1); for (n=2, 22, forstep (w=v+s=(b=2)^#digits(v,b), oo, s, if (isprime(w), print1 (", "v=w); break)))
Previous Showing 11-15 of 15 results.

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