A086801 -id:A086801 - cp's OEIS frontend

A173064 a(n) = prime(n) - 5.

0, 2, 6, 8, 12, 14, 18, 24, 26, 32, 36, 38, 42, 48, 54, 56, 62, 66, 68, 74, 78, 84, 92, 96, 98, 102, 104, 108, 122, 126, 132, 134, 144, 146, 152, 158, 162, 168, 174, 176, 186, 188, 192, 194, 206, 218, 222, 224, 228, 234, 236, 246, 252, 258, 264, 266, 272, 276, 278, 288, 302, 306, 308, 312, 326, 332, 342, 344, 348, 354, 362, 368, 374, 378, 384, 392, 396, 404

Offset: 3

Vladimir Joseph Stephan Orlovsky, Nov 21 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 3..10000

Cf. A086801, A113935, A175222.

[NthPrime(n) - 5: n in [3..100]]; // G. C. Greubel, May 19 2019

Mathematica
```
Prime[Range[3,120]] - 5
```

{a(n) = prime(n) - 5}; \\ G. C. Greubel, May 19 2019

[nth_prime(n) - 5 for n in (3..100)] # G. C. Greubel, May 19 2019

A369657 a(n) = A356253(n) - A003415(n).

Original entry on oeis.org

1, 1, 2, 0, 4, 1, 6, 0, 3, 3, 10, 0, 12, 5, 7, 0, 16, 0, 18, 0, 11, 9, 22, 0, 15, 11, 0, 0, 28, 0, 30, 0, 19, 15, 23, 0, 36, 17, 23, 0, 40, 1, 42, 0, 6, 21, 46, 0, 35, 5, 31, 0, 52, 0, 39, 0, 35, 27, 58, 0, 60, 29, 12, 48, 47, 5, 66, 0, 43, 11, 70, 0, 72, 35, 20, 0, 59, 7, 78, 0, 0, 39, 82, 0, 63, 41, 55, 0, 88, 0, 71

Offset: 1

Antti Karttunen, Feb 08 2024

nonn

From M. F. Hasler, Feb 14 2024: (Start)
a(n) = 0 for most n divisible by 4, except n = 64, 96, 128, 144, 160, 192, 216, 224, 240, 256, ... These exceptions include all proper multiples of 32 but also some other multiples of 4: 9*16, 27*8, 15*16, 21*16, ...
a(n) = 0 also for some n not a multiple of 4, namely 18*(6k + 1) for all k >= 0 except 2604, 18229, 33854, ... and 27*(4k + 1) for k >= 0 different from 101, 182, 236, ..., and others.
a(n) = 48 for all numbers of the form 32*p where p is prime, and for n = 171. (Are there any others?) This is by far the most frequent nonzero value: it can be seen as a horizontal line in the graph of the sequence.
a(n) = 11 for n = 5*709, 2*2833, 2*37*83, 2*29*107, 2*23*137, 2*17*191, 2*11*317, 2*7*569, 2*5*947, 2*3*2837, 2*3*53*67, ... This appears to be the second most frequent nonzero value. (End)

Antti Karttunen, Table of n, a(n) for n = 1..30030

Cf. A003415, A086801, A356253.

A356253(n) = vecmax(Vec(vecprod([(x + f[1])^f[2] | f<-factor(n)~])))
A003415(n) = if(n>1, vecsum([n/f[1]*f[2] | f<-factor(n)~]), 0)
A369657(n) = A356253(n)-A003415(n) \\ This and above edited by M. F. Hasler, Feb 14 2024

a(9*prime(n)) = 3*A086801(n) for n > 1. - Thomas Scheuerle, Feb 14 2024

A119981 a(n) = 1 iff number congruent to {2, 4} mod 6 is equal to prime minus 3, otherwise a(n)=0.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0

Offset: 1

Giovanni Teofilatto, Aug 03 2006

a(n) = 1 iff A047235(n) + 3 = A086801(n).

Cf. A047235, A086801.

A144840 Numbers k such that the three numbers k-1, k+3 and k+5 are all prime.

Original entry on oeis.org

8, 14, 38, 68, 98, 104, 194, 224, 278, 308, 458, 614, 824, 854, 878, 1088, 1298, 1424, 1448, 1484, 1664, 1694, 1784, 1868, 1874, 1994, 2084, 2138, 2378, 2684, 2708, 2798, 3164, 3254, 3458, 3464, 3848, 4154, 4514, 4784, 5228, 5414, 5438, 5648, 5654, 5738

Offset: 1

Giovanni Teofilatto, Sep 23 2008

Eric Weisstein's World of Mathematics, Prime Triplet.

Cf. A022005, A086801, A144834.

Cf. A098413, A144842.

from sympy import isprime
def ok(n): return n > 4 and isprime(n-1) and isprime(n+3) and isprime(n+5)
print(list(filter(ok, range(5739)))) # Michael S. Branicky, Aug 14 2021

a(n) = A022005(n) + 1. - R. J. Mathar, Sep 24 2008

Definition edited and extended by R. J. Mathar, Sep 24 2008

A146538 Even numbers n such that n+3 is not a prime.

Original entry on oeis.org

6, 12, 18, 22, 24, 30, 32, 36, 42, 46, 48, 52, 54, 60, 62, 66, 72, 74, 78, 82, 84, 88, 90, 92, 96, 102, 108, 112, 114, 116, 118, 120, 122, 126, 130, 132, 138, 140, 142, 144, 150, 152, 156, 158, 162, 166, 168, 172, 174, 180, 182, 184, 186, 192, 198, 200, 202, 204, 206

Offset: 1

Giovanni Teofilatto, Oct 31 2008

Cf. A086801.

Select[2*Range[150],!PrimeQ[#+3]&] (* Harvey P. Dale, Oct 15 2012 *)

54 and 66 inserted, 7274 split, 78 inserted, 176 removed by R. J. Mathar, Dec 04 2008

A177357 Number of positive squares <= prime(n) - 3.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19

Offset: 2

Giovanni Teofilatto, May 07 2010

nonn

Cf. A000006.

A000196 := proc(n) floor(sqrt(n)) ; end proc:
A086801 := proc(n) ithprime(n)-3 ; end proc:
A177357 := proc(n) A000196(A086801(n)) ; end proc: seq(A177357(n),n=2..90) ; # R. J. Mathar, May 09 2010

Floor[Sqrt[Prime[Range[2,80]]-3]] (* Harvey P. Dale, Dec 15 2018 *)

a(n) = A000196(A086801(n)). - R. J. Mathar, May 09 2010

Edited by N. J. A. Sloane, May 08 2010
More terms from R. J. Mathar, May 09 2010
Reference redirected to a valid A-number by R. J. Mathar, May 09 2010

A370204 a(n) is the smallest number k for which the length of the central extent of width 0 in the symmetric representation of sigma, SRS(k), equals 2n and is -1 if there is no such extent of length 2n.

Original entry on oeis.org

3, 5, 7, 22, 11, 13, 34, 17, 19, 46, 23, 87, 58, 29, 31, 111, 74, 37, 82, 41, 43, 94, 47, 159, 106, 53, 177, 118, 59, 61, 201, 134, 67, 142, 71, 73, 237, 158, 79, 166, 83, 267, 178, 89, 388, 291, 194, 97, 202, 101, 103, 214, 107, 109, 226, 113, 889, 762, 635, 508, 381, 254, 127, 262, 131, 411

Offset: 0

Hartmut F. W. Hoft, Feb 11 2024

nonn

Indices of the first occurrence of value 2*n in A368945.
SRS(a(n)) has an even number of parts.
The maximum possible central 0 width extent in SRS(n) for odd numbers n is 2*n - (n+1) - 2 = n - 3. This is achieved only by odd prime numbers which form a subsequence.
Conjecture: a(n) != -1 for all n >= 0.

			a(2) = 7 since prime 7 is the smallest number whose central extent of width 0 equals 4.
a(3) = 22 since 22 is the smallest number whose central extent of width 0 equals 6.

Cf. A000040, A071561, A071562, A086801, A100484, A154115, A235791, A237048, A237270, A237593, A249223, A368945.

(* Function extent0[ ] is defined in A368945 *)
smallest[n_] := NestWhile[#+1&, n, extent0[#]!=n&]/;EvenQ[n]
a370204[n_] := Map[smallest[2#]&, Range[0, n]]
a370204[65]

a(n) = min( k : A368945(k) = 2*n ), 0<=n, if the minimum exists, a(n) = -1 otherwise.

A368945(a(k)) = 2 * k, k>=0 and a(k) != -1.

A144206 Numbers A141427(k) such that the three numbers A141427(k) -/+ 3 and A141427(k) + 1 are all prime.

Original entry on oeis.org

10, 16, 40, 70, 100, 106, 196, 226, 280, 310, 460, 616, 826, 856, 880, 1090, 1300, 1426, 1450, 1486, 1666, 1696, 1786, 1870, 1876, 1996, 2086, 2140, 2380, 2686, 2710, 2800, 3166, 3256, 3460, 3466, 3850, 4156, 4516, 4786, 5230, 5416, 5440, 5650, 5656, 5740, 6550, 6826, 7210, 7756, 7876, 8290, 8626

Offset: 1

Giovanni Teofilatto, Sep 14 2008

Cf. A086801, A141427.

Corrected definition and extended. - R. J. Mathar, Sep 18 2008

Corrected A-number typo in the definition. - R. J. Mathar, Oct 14 2008

cp's OEIS Frontend

A173064 a(n) = prime(n) - 5.

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Magma

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A369657 a(n) = A356253(n) - A003415(n).

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A119981 a(n) = 1 iff number congruent to {2, 4} mod 6 is equal to prime minus 3, otherwise a(n)=0.

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A144840 Numbers k such that the three numbers k-1, k+3 and k+5 are all prime.

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Python

Formula

Extensions

A146538 Even numbers n such that n+3 is not a prime.

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Programs

Mathematica

Extensions

A177357 Number of positive squares <= prime(n) - 3.

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Maple

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Formula

Extensions

A370204 a(n) is the smallest number k for which the length of the central extent of width 0 in the symmetric representation of sigma, SRS(k), equals 2*n and is -1 if there is no such extent of length 2*n.

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Mathematica

Formula

A144206 Numbers A141427(k) such that the three numbers A141427(k) -/+ 3 and A141427(k) + 1 are all prime.

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Extensions

A370204 a(n) is the smallest number k for which the length of the central extent of width 0 in the symmetric representation of sigma, SRS(k), equals 2n and is -1 if there is no such extent of length 2n.