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 16 results. Next

A089711 Primes arising in A089710.

Original entry on oeis.org

3, 13, 613, 9613, 49613, 2049613, 132049613, 29132049613, 1929132049613, 21929132049613, 721929132049613, 18721929132049613, 1218721929132049613, 411218721929132049613, 36411218721929132049613
Offset: 1

Views

Author

Amarnath Murthy, Nov 17 2003

Keywords

Crossrefs

Cf. A089710.

Extensions

More terms from Ray Chandler, Nov 21 2003

A089560 a(1) = 1. For n > 1, a(n) is the least unused number such that the concatenation a(n)a(n-1)...a(2)a(1) is prime.

Original entry on oeis.org

1, 3, 4, 5, 7, 14, 9, 6, 57, 13, 18, 17, 16, 12, 20, 82, 42, 21, 45, 78, 98, 33, 133, 50, 28, 41, 124, 36, 44, 19, 80, 40, 75, 63, 372, 168, 179, 85, 84, 128, 64, 302, 151, 248, 10, 69, 123, 11, 54, 31, 149, 34, 185, 51, 213, 43, 282, 105, 125, 237, 55, 174, 96, 438, 215, 61
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Comments

Is this a rearrangement of the natural numbers?

Crossrefs

Cf. A089710, A089711, A089561-A089573.

Extensions

Edited by Charles R Greathouse IV, Apr 29 2010

A089573 Primes arising in A089572.

Original entry on oeis.org

19, 419, 5419, 35419, 735419, 9735419, 159735419, 14159735419, 114159735419, 60114159735419, 2660114159735419, 282660114159735419, 6282660114159735419, 206282660114159735419, 13206282660114159735419
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Crossrefs

Cf. A089710, A089711, A089560-A089572.

A171154 Smallest prime whose decimal expansion begins with concatenation of first n primes in descending order.

Original entry on oeis.org

2, 3203, 5323, 75323, 11753221, 131175329, 171311753203, 19171311753229, 231917131175321, 292319171311753231, 3129231917131175327, 3731292319171311753239, 41373129231917131175321, 43413731292319171311753233, 4743413731292319171311753269, 534743413731292319171311753223
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 04 2009

Keywords

Comments

Sequence is conjectured to be infinite.
a(n) = "prime(n)...prime(1) R(n)".
R(n) for n>1: 03, 3, 3, 21, 9, 03, 29, 1, 31, 7, 39, 1, 33, 69, 23, 3, 59, 27, ...
It is conjectured that R(n)=1 for infinite many n.

Examples

			a(1) = 2 = prime(1) is the exceptional case, because no R(1).
a(2) = 3203 = prime(453) = "32 03", R(2)="03".
a(5) = 11753221 = prime(772902) = "prime(5)...prime(1) 21", R(5)=21.

References

  • Leonard E. Dickson, History of the Theory of numbers, vol. I, Dover Publications 2005.

Links

Crossrefs

Cf. A000040, A066065, A019518, A089710, A053546.

Programs

  • Python
    from sympy import isprime, primerange, prime
def a(n):
    if n == 1: return 2
    c = int("".join(map(str, [p for p in primerange(2, prime(n)+1)][::-1])))
    pow10 = 10
    while True:
        c *= 10
        for b in range(1, pow10, 2):
            if b%5 == 0: continue
            if isprime(c+b):
                return c+b
        pow10 *= 10
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Mar 12 2022

Extensions

a(14) and beyond from Michael S. Branicky, Mar 12 2022

A089564 a(1) = 9. For n > 1, a(n) is the least unused number such that the decimal concatenation a(n)a(n-1)...a(2)a(1) is prime.

Original entry on oeis.org

9, 1, 4, 5, 3, 7, 12, 11, 13, 42, 26, 10, 17, 16, 20, 82, 29, 78, 57, 27, 28, 66, 45, 6, 69, 33, 236, 40, 116, 237, 196, 65, 133, 90, 60, 72, 80, 61, 126, 24, 153, 68, 88, 122, 43, 156, 231, 285, 125, 177, 249, 106, 36, 147, 23, 208, 483, 138, 281, 63, 108, 22, 38, 75, 159
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Comments

Is this a permutation of the positive integers?
The sequence is infinite by Dirichlet's theorem; Linnik's theorem gives an effectively computable bound on its members. Using Xylouris's version with L <= 5.2, a(n) = 9^(5.2^(n + O(log n))). - Charles R Greathouse IV, Apr 27 2010

Crossrefs

Cf. A089710, A089711, A089560-A089573.

A089561 Concatenations arising in A089560.

Original entry on oeis.org

1, 31, 431, 5431, 75431, 1475431, 91475431, 691475431, 57691475431, 1357691475431, 181357691475431, 17181357691475431, 1617181357691475431, 121617181357691475431, 20121617181357691475431
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Crossrefs

Cf. A089710, A089711, A089560-A089573.

A089562 a(1) = 7. For n > 1, a(n) is the least unused number such that every concatenation a(n)a(n-1)...a(2)a(1) is prime.

Original entry on oeis.org

7, 1, 3, 6, 2, 21, 10, 9, 8, 37, 20, 25, 29, 72, 28, 30, 27, 23, 39, 19, 51, 32, 22, 54, 42, 35, 24, 73, 36, 120, 44, 186, 4, 26, 126, 171, 70, 33, 18, 60, 113, 99, 81, 76, 47, 108, 91, 170, 159, 49, 65, 114, 238, 185, 285, 34, 98, 312, 63, 183, 15, 205, 230, 198, 310, 524
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Comments

Is this a rearrangement of the natural numbers?

Crossrefs

Cf. A089710, A089711, A089560-A089573.

Extensions

Edited by Charles R Greathouse IV, Apr 29 2010

A089566 a(1) = 11. For n > 1, a(n) is the least unused number such that every concatenation a(n)a(n-1)...a(2)a(1) is prime.

Original entry on oeis.org

11, 2, 4, 3, 5, 9, 1, 30, 6, 20, 16, 8, 24, 15, 13, 39, 36, 56, 64, 72, 29, 49, 27, 60, 54, 63, 65, 45, 12, 99, 28, 47, 88, 51, 83, 31, 59, 94, 336, 108, 182, 204, 184, 38, 37, 188, 210, 91, 62, 10, 224, 202, 128, 115, 66, 111, 156, 566, 43, 255, 279, 315, 180, 257, 102, 118
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Comments

Is this a rearrangement of the natural numbers?

Crossrefs

Cf. A089710, A089711, A089560-A089573.

Extensions

Edited by Charles R Greathouse IV, Apr 29 2010

A089568 a(1) = 13. For n > 1, a(n) is the least unused number such that every concatenation a(n)a(n-1)...a(2)a(1) is prime.

Original entry on oeis.org

13, 1, 2, 19, 3, 8, 15, 18, 10, 17, 45, 24, 22, 11, 37, 5, 30, 39, 81, 6, 76, 57, 69, 56, 84, 36, 49, 48, 38, 63, 148, 27, 75, 239, 31, 50, 171, 67, 116, 282, 42, 175, 23, 55, 236, 70, 278, 73, 90, 140, 91, 9, 210, 174, 126, 105, 89, 94, 224, 34, 114, 26, 133, 143, 54, 241
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Comments

Is this a rearrangement of the natural numbers?

Crossrefs

Cf. A089710, A089711, A089560-A089573.

Extensions

Edited by Charles R Greathouse IV, Apr 29 2010

A089570 a(1) = 17. For n > 1, a(n) is the least unused number such that every concatenation a(n)a(n-1)...a(2)a(1) is prime.

Original entry on oeis.org

17, 3, 6, 2, 1, 21, 35, 43, 23, 34, 47, 10, 26, 4, 14, 15, 12, 40, 18, 54, 51, 5, 27, 9, 132, 63, 166, 98, 78, 24, 30, 58, 105, 71, 75, 57, 70, 42, 11, 19, 38, 217, 285, 36, 77, 64, 56, 259, 45, 93, 102, 60, 122, 66, 96, 103, 267, 255, 92, 91, 276, 152, 208, 204, 90, 138
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Comments

Is this a rearrangement of the natural numbers?

Crossrefs

Cf. A089710, A089711, A089560-A089573.

Extensions

Edited by Charles R Greathouse IV, Apr 29 2010
Showing 1-10 of 16 results. Next

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