A272160 -id:A272160 - cp's OEIS frontend

A283903 Relative of Hofstadter Q-sequence.

11, 20, 6, 6, 6, 20, 11, 20, 6, 6, 6, 20, 11, 6, 12, 12, 12, 20, 11, 6, 18, 18, 12, 40, 11, 12, 24, 18, 12, 40, 11, 18, 30, 18, 18, 40, 11, 24, 30, 18, 18, 80, 11, 30, 30, 24, 24, 80, 11, 30, 36, 30, 24, 80, 11, 30, 48, 24, 24, 80, 11, 36, 54, 24, 24, 160, 11, 48, 42, 36, 30, 120, 11, 54, 42

Offset: 1

Nathan Fox, Mar 19 2017

This sequence is defined by a(n) = 0 for n <= 0; a(1) = 11, a(2) = 20, a(3) = 6, a(4) = 6, a(5) = 6, a(6) = 20, a(7) = 11, a(8) = 20, a(9) = 6, a(10) = 6, a(11) = 6, a(12) = 20, a(13) = 11, a(14) = 6, a(15) = 12, a(16) = 12, a(17) = 12, a(18) = 20; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).
Similar to Hofstadter's Q-sequence A005185 but with different starting values.
For as long as it exists, this sequence has a similar structure to A272160. That sequence consists of five interleaved sequences: four chaotic sequences and a sequence of all 4's. This sequence consists of six interleaved sequences: five chaotic sequences and a sequence of all 11's.
If the 20's in the initial condition are each replaced by larger numbers, the general structure of this sequence does not change.
This sequence has exactly 2179 terms, since a(2179)=0 and computing a(2180) would refer to itself.

Nathan Fox, Table of n, a(n) for n = 1..2179

Cf. A005185, A272610, A284053, A284054.

A283903:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 11: elif n = 2 then 20: elif n = 3 then 6: elif n = 4 then 6: elif n = 5 then 6: elif n = 6 then 20: elif n = 7 then 11: elif n = 8 then 20: elif n = 9 then 6: elif n = 10 then 6: elif n = 11 then 6: elif n = 12 then 20: elif n = 13 then 11: elif n = 14 then 6: elif n = 15 then 12: elif n = 16 then 12: elif n = 17 then 12: elif n = 18 then 20: else A283903(n-A283903(n-1)) + A283903(n-A283903(n-2)): fi: end:

A284054 Relative of Hofstadter Q-sequence.

Original entry on oeis.org

7, 26, 8, 8, 8, 8, 8, 26, 7, 8, 16, 16, 16, 16, 16, 26, 7, 16, 24, 8, 16, 24, 8, 26, 7, 24, 16, 24, 24, 16, 24, 52, 7, 16, 48, 8, 24, 32, 24, 52, 7, 48, 8, 8, 48, 32, 16, 78, 7, 8, 16, 16, 48, 40, 24, 78, 7, 16, 24, 16, 72, 32, 24, 104, 7, 24, 24, 16, 96, 40, 24, 130, 7, 24, 32

Offset: 1

Nathan Fox, Mar 19 2017

nonn

This sequence is defined by a(n) = 0 for n <= 0; a(1) = 7, a(2) = 26, a(3) = 8, a(4) = 8, a(5) = 8, a(6) = 8, a(7) = 8, a(8) = 26, a(9) = 7, a(10) = 8, a(11) = 16, a(12) = 16, a(13) = 16, a(14) = 16, a(15) = 16, a(16) = 26; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).
Similar to Hofstadter's Q-sequence A005185 but with different starting values.
Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.
This sequence has a similar structure to A272160. That sequence consists of five interleaved sequences: four chaotic sequences and a sequence of all 4's. This sequence appears to consist eventually of eight interleaved sequences: four chaotic sequences, a sequence of all 7's, a sequence of mostly 32's and an few 40's, a sequence of all 24's, and a rapidly growing sequence with successive terms satisfying either the recurrence A(k) = A(k-3) + A(k-4) or the recurrence A(k) = A(k-3) + A(k-5).
If the 26's in the initial condition are each replaced by larger numbers, the general structure of this sequence does not change.

Nathan Fox, Table of n, a(n) for n = 1..10000

Cf. A005185, A272610, A283903, A284053.

A284054:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 7: elif n = 2 then 26: elif n = 3 then 8: elif n = 4 then 8: elif n = 5 then 8: elif n = 6 then 8: elif n = 7 then 8: elif n = 8 then 26: elif n = 9 then 7: elif n = 10 then 8: elif n = 11 then 16: elif n = 12 then 16: elif n = 13 then 16: elif n = 14 then 16: elif n = 15 then 16: elif n = 16 then 26: else A284054(n-A284054(n-1)) + A284054(n-A284054(n-2)): fi: end:

from functools import lru_cache
@lru_cache(maxsize=None)
def a(n):
    if n <= 0: return 0
    if n < 17:
        return [7, 26, 8, 8, 8, 8, 8, 26, 7, 8, 16, 16, 16, 16, 16, 26][n-1]
    return a(n - a(n-1)) + a(n - a(n-2))
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Jul 26 2021

A247163 Nonnegative numbers n such that abs(1/4 (n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316)) is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 59, 60, 61, 64, 67, 68, 69, 74, 75, 76

Offset: 1

Robert Price, May 04 2016

nonn

62 is the smallest number not in this sequence.

			4 is in this sequence since abs(1/4 (n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316)) = abs((1024 - 34048 + 430656 - 2534064 + 6881176 - 6823316)/4) = 519643 is prime.

Robert Price, Table of n, a(n) for n = 1..2328
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A272401, A272438, A272444, A272410, A272555, A272710.

Select[Range[0, 100], PrimeQ[1/4 (#^5 - 133#^4 + 6729#^3 - 158379#^2 + 1720294# - 6823316)] &]

A267069 Nonnegative numbers n such that abs(103n^2 - 4707n + 50383) is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 53, 54, 57, 59, 60, 61, 63, 64, 65, 66, 67, 69, 73, 74, 76, 77, 80

Offset: 1

Robert Price, Apr 28 2016

nonn

43 is the smallest number not in this sequence.

See A267252 for more information. - Hugo Pfoertner, Dec 13 2019

			4 is in this sequence since 103*4^2 - 4707*4 + 50383  = 1648-18828+50383 = 33203 is prime.

Robert Price, Table of n, a(n) for n = 1..3885
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A267252.

Select[Range[0, 100], PrimeQ[103#^2 - 4707# + 50383 ] &]

lista(nn) = for(n=0, nn, if(isprime(abs(103*n^2-4707*n+50383)), print1(n, ", "))); \\ Altug Alkan, Apr 28 2016, corrected by Hugo Pfoertner, Dec 13 2019

Title corrected by Hugo Pfoertner, Dec 13 2019

A272813 Nonnegative numbers n such that n^2 - 79n + 1601 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66

Offset: 1

Robert Price, May 06 2016

nonn

80 is the smallest number not in this sequence.

See A005846 for the corresponding primes.

			4 is in this sequence since 4^2 - 79*4 + 1601 = 16-316+1601 = 1301 is prime.

Robert Price, Table of n, a(n) for n = 1..4179
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A272401, A272438, A272444, A272410, A272555, A272710, A005846.

Select[Range[0, 100], PrimeQ[#^2 - 79# + 1601 ] &]

lista(nn) = for(n=0, nn, if(isprime(n^2-79*n+1601), print1(n, ", "))); \\ Altug Alkan, May 06 2016

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A283903 Relative of Hofstadter Q-sequence.

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A284054 Relative of Hofstadter Q-sequence.

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A247163 Nonnegative numbers n such that abs(1/4 (n^5 - 133n^4 + 6729n^3 - 158379n^2 + 1720294n - 6823316)) is prime.

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A267069 Nonnegative numbers n such that abs(103*n^2 - 4707*n + 50383) is prime.

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A272813 Nonnegative numbers n such that n^2 - 79n + 1601 is prime.

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A267069 Nonnegative numbers n such that abs(103n^2 - 4707n + 50383) is prime.