A175222 -id:A175222 - cp's OEIS frontend

A052147 a(n) = prime(n) + 2.

4, 5, 7, 9, 13, 15, 19, 21, 25, 31, 33, 39, 43, 45, 49, 55, 61, 63, 69, 73, 75, 81, 85, 91, 99, 103, 105, 109, 111, 115, 129, 133, 139, 141, 151, 153, 159, 165, 169, 175, 181, 183, 193, 195, 199, 201, 213, 225, 229, 231, 235, 241, 243, 253, 259

Offset: 1

Simon Colton (simonco(AT)cs.york.ac.uk), Jan 24 2000

A048974, A052147, A067187 and A088685 are very similar after dropping terms less than 13. - Eric W. Weisstein, Oct 10 2003
A117530(n,2) = a(n) for n>1. - Reinhard Zumkeller, Mar 26 2006
a(n) = A000040(n) + 2 = A008864(n) + 1 = A113395(n) - 1 = A175221(n) - 2 = A175222(n) - 3 = A139049(n) - 4 = A175223(n) - 5 = A175224(n) - 6 = A140353(n) - 7 = A175225(n) - 8. - Jaroslav Krizek, Mar 06 2010
Left edge of the triangle in A065342. - Reinhard Zumkeller, Jan 30 2012
Union of A006512 and A107986. - David James Sycamore, Jul 08 2018

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

A139690 is a subsequence.

Cf. A040976, A000040.

Filtered([1..300], k-> IsPrime(k) ) + 2; # G. C. Greubel, May 20 2019

a052147 = (+ 2) . a000040  -- Reinhard Zumkeller, Jul 03 2015

[p+2: p in PrimesUpTo(400)]; // Vincenzo Librandi, Nov 27 2013

seq(ithprime(n)+2,n=1..55); # Muniru A Asiru, Jul 08 2018

Prime[Range[70]]+2 (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

a(n)=prime(n)+2 \\ Charles R Greathouse IV, Jan 19 2017

[nth_prime(n) +2 for n in (1..70)] # G. C. Greubel, May 20 2019

A113935 a(n) = prime(n) + 3.

Original entry on oeis.org

5, 6, 8, 10, 14, 16, 20, 22, 26, 32, 34, 40, 44, 46, 50, 56, 62, 64, 70, 74, 76, 82, 86, 92, 100, 104, 106, 110, 112, 116, 130, 134, 140, 142, 152, 154, 160, 166, 170, 176, 182, 184, 194, 196, 200, 202, 214, 226, 230, 232, 236, 242, 244, 254, 260, 266, 272, 274

Offset: 1

Jorge Coveiro, Jan 30 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A098090, A116366.

List([1..70], n-> Primes[n]+3); # G. C. Greubel, May 18 2019

[p+3: p in PrimesUpTo(500)]; // Vincenzo Librandi, Nov 27 2013

Prime[Range[70]]+3 (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

PARI
```
for(x=1,100,print1(prime(x)+3,","))
```

[nth_prime(n)+3 for n in (1..70)] # G. C. Greubel, May 18 2019

a(n) = A116366(n-1,1) for n>1. - Reinhard Zumkeller, Feb 06 2006
a(n) = 2*A098090(n-1) for n > 1. - Reinhard Zumkeller, Sep 14 2006
a(n) = A000040(n) + 3 = A008864(n) + 2 = A052147(n) + 1 = A175221(n) - 1 = A175222(n) - 2 = A139049(n) - 3 = A175223(n) - 4 = A175224(n) - 5 = A140353(n) - 6 = A175225(n) - 7. - Jaroslav Krizek, Mar 06 2010

A140353 a(n) = prime(n) + 9.

Original entry on oeis.org

11, 12, 14, 16, 20, 22, 26, 28, 32, 38, 40, 46, 50, 52, 56, 62, 68, 70, 76, 80, 82, 88, 92, 98, 106, 110, 112, 116, 118, 122, 136, 140, 146, 148, 158, 160, 166, 172, 176, 182, 188, 190, 200, 202, 206, 208, 220, 232, 236, 238, 242, 248, 250, 260, 266, 272, 278, 280, 286

Offset: 1

Odimar Fabeny, May 30 2008

a(n) = A000040(n) + 9 = A008864(n) + 8 = A052147(n) + 7 = A113395(n) + 6 = A175221(n) + 5 = A175222(n) + 4 = A139049(n) + 3 = A175223(n) + 2 = A175224(n) + 1 = A175225(n) - 1. - Jaroslav Krizek, Mar 06 2010

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A139049

Filtered([1..300], k-> IsPrime(k) ) +9 # G. C. Greubel, May 20 2019

[NthPrime(n)+9: n in [1..70]]; // G. C. Greubel, May 20 2019

9 + Prime[Range[70]] (* G. C. Greubel, May 20 2019 *)

PARI
```
A140353(n) = prime(n)+9
```

[nth_prime(n) +9 for n in (1..70)] # G. C. Greubel, May 20 2019

Edited by Michael B. Porter, Jan 28 2010

A175221 a(n) = prime(n) + 4.

Original entry on oeis.org

6, 7, 9, 11, 15, 17, 21, 23, 27, 33, 35, 41, 45, 47, 51, 57, 63, 65, 71, 75, 77, 83, 87, 93, 101, 105, 107, 111, 113, 117, 131, 135, 141, 143, 153, 155, 161, 167, 171, 177, 183, 185, 195, 197, 201, 203, 215, 227, 231, 233, 237, 243, 245, 255, 261, 267, 273, 275

Offset: 1

Jaroslav Krizek, Mar 06 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Filtered([1..300], k-> IsPrime(k) ) + 4; # G. C. Greubel, May 20 2019

[(p+4):p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

Prime[Range[60]]+4 (* Harvey P. Dale, Jan 01 2013 *)

{a(n) = prime(n) + 4}; \\ G. C. Greubel, May 20 2019

[nth_prime(n) + 4 for n in (1..60)] # G. C. Greubel, May 20 2019

a(n) = A000040(n) + 4 = A008864(n) + 3 = A052147(n) + 2 = A113395(n) + 1.
a(n) = A175222(n) - 1 = A139049(n) - 2 = A175223(n) - 3.
a(n) = A175224(n) - 4 = A140353(n) - 5 = A175225(n) - 6.

More terms from Vincenzo Librandi, Mar 14 2010

A139049 a(n) = prime(n) + 6.

Original entry on oeis.org

8, 9, 11, 13, 17, 19, 23, 25, 29, 35, 37, 43, 47, 49, 53, 59, 65, 67, 73, 77, 79, 85, 89, 95, 103, 107, 109, 113, 115, 119, 133, 137, 143, 145, 155, 157, 163, 169, 173, 179, 185, 187, 197, 199, 203, 205, 217, 229, 233, 235, 239, 245, 247, 257, 263, 269, 275, 277

Offset: 1

Odimar Fabeny, Jun 02 2008

a(n) = A000040(n) + 6 = A008864(n) + 5 = A052147(n) + 4 = A113395(n) + 3 = A175221(n) + 2 = A175222(n) + 1 = A175223(n) - 1 = A175224(n) - 2 = A140353(n) - 3 = A175225(n) - 4. - Jaroslav Krizek, Mar 06 2010

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A140353.

Filtered([1..300], k-> IsPrime(k) ) + 6; # G. C. Greubel, May 20 2019

[NthPrime(n)+6: n in [1..70]]; // G. C. Greubel, May 20 2019

A139049:=n->ithprime(n)+6: seq(A139049(n), n=1..100); # Wesley Ivan Hurt, Apr 18 2017

6+Prime[Range[70]] (* G. C. Greubel, May 20 2019 *)

PARI
```
A139049(n) = prime(n)+6
```

[nth_prime(n) +6 for n in (1..70)] # G. C. Greubel, May 20 2019

Edited by Michael B. Porter, Jan 28 2010

A175223 a(n) = prime(n) + 7.

Original entry on oeis.org

9, 10, 12, 14, 18, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 60, 66, 68, 74, 78, 80, 86, 90, 96, 104, 108, 110, 114, 116, 120, 134, 138, 144, 146, 156, 158, 164, 170, 174, 180, 186, 188, 198, 200, 204, 206, 218, 230, 234, 236, 240, 246, 248, 258, 264, 270, 276, 278

Offset: 1

Jaroslav Krizek, Mar 06 2010

a(n) = A000040(n) + 7 = A008864(n) + 6 = A052147(n) + 5 = A113395(n) + 4 = A175221(n) + 3 = A175222 (n) + 2 = A139049(n) + 1 = A175224(n) - 1 = A140353(n) - 2 = A175225(n) - 3.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Filtered([1..300], k-> IsPrime(k) ) + 7; # G. C. Greubel, May 20 2019

[p+7: p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

Prime[Range[70]] + 7 (* Vincenzo Librandi, Nov 27 2013 *)

{a(n) = prime(n) + 7}; \\ G. C. Greubel, May 20 2019

[nth_prime(n) + 7 for n in (1..70)] # G. C. Greubel, May 20 2019

More terms from Vincenzo Librandi, Mar 14 2010

A175224 a(n) = prime(n) + 8.

Original entry on oeis.org

10, 11, 13, 15, 19, 21, 25, 27, 31, 37, 39, 45, 49, 51, 55, 61, 67, 69, 75, 79, 81, 87, 91, 97, 105, 109, 111, 115, 117, 121, 135, 139, 145, 147, 157, 159, 165, 171, 175, 181, 187, 189, 199, 201, 205, 207, 219, 231, 235, 237, 241, 247, 249, 259, 265, 271, 277, 279

Offset: 1

Jaroslav Krizek, Mar 06 2010

nonn

a(n) = A000040(n) + 8 = A008864(n) + 7 = A052147(n) + 6 = A113395(n) + 5 = A175221(n) + 4 = A175222(n) + 3 = A139049(n) + 2 = A175223(n) + 1 = A140353(n) - 1 = A175225(n) - 2.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000040, A008864, A052147, A113395, A175221, A175222, A139049, A175223, A140353, A175225.

Filtered([1..300], k-> IsPrime(k) ) + 8; # G. C. Greubel, May 20 2019

[(p+8): p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

Prime[Range[60]]+8 (* Harvey P. Dale, Mar 02 2015 *)

{a(n) = prime(n) + 8}; \\ G. C. Greubel, May 20 2019

[nth_prime(n) + 8 for n in (1..60)] # G. C. Greubel, May 20 2019

More terms from Vincenzo Librandi, Mar 14 2010

A175225 a(n) = prime(n) + 10.

Original entry on oeis.org

12, 13, 15, 17, 21, 23, 27, 29, 33, 39, 41, 47, 51, 53, 57, 63, 69, 71, 77, 81, 83, 89, 93, 99, 107, 111, 113, 117, 119, 123, 137, 141, 147, 149, 159, 161, 167, 173, 177, 183, 189, 191, 201, 203, 207, 209, 221, 233, 237, 239, 243, 249, 251, 261, 267, 273, 279, 281

Offset: 1

Jaroslav Krizek, Mar 06 2010

nonn

a(n) = A000040(n) + 10 = A008864(n) + 9 = A052147(n) + 8 = A113395(n) + 7 = A175221(n) + 6 = A175222(n) + 5 = A139049(n) + 4 = A175223(n) + 3 = A175224(n) + 2 = A140353(n) + 1.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000040, A008864, A052147, A113395, A139049, A140353, A175221, A175222, A175223, A175224.

Filtered([1..300], k-> IsPrime(k) ) + 10; # G. C. Greubel, May 21 2019

[(p+10):p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

10 + Prime[Range[70]] (* G. C. Greubel, May 21 2019 *)

{a(n) = prime(n) + 10}; \\ G. C. Greubel, May 21 2019

[nth_prime(n) + 10 for n in (1..70)] # G. C. Greubel, May 21 2019

More terms from Vincenzo Librandi, Mar 14 2010

A297925 Even numbers k such that k - 5 is prime but k - 3 is not prime.

Original entry on oeis.org

12, 18, 24, 28, 36, 42, 48, 52, 58, 66, 72, 78, 84, 88, 94, 102, 108, 114, 118, 132, 136, 144, 156, 162, 168, 172, 178, 186, 198, 204, 216, 228, 234, 238, 246, 256, 262, 268, 276, 282, 288, 298, 312, 318, 322, 336, 342, 354, 358, 364, 372, 378, 384, 388, 394, 402, 406, 414, 426, 438, 444, 448, 454

Offset: 1

David James Sycamore, Jan 08 2018

nonn

Even numbers that are the sum of 5 and another prime, but not the sum of 3 and another prime. For n >= 1, a(n) - 5 = A049591(n), a(n) - 3 = A107986(n+1).
Let r(n) = a(n) - 5, Then r(n) is the greatest prime < a(n), and therefore A056240(a(n)) = 5*r(n). Furthermore, since r(n) + 2 must be composite, A056240(a(n)) = 5*A049591(n).
The terms in this sequence, combined with those in A298366 and A298252 form a partition of A005843(n);n>=3 (nonnegative even numbers>=6). This is because any even integer n>=6 satisfies either (i) n-3 is prime, (ii) n-5 is prime but n-3 is composite, or (iii) both n-5 and n-3 are composite.

			12 is a term because 12 - 5 = 7 is prime, and 12 - 3 = 9 is composite. Also A049591(1)+5=7+5=12 and A107986(2)+3=9+3=12.
18 is a term because 18 - 5 = 13 is prime, and 18 - 3 = 15 is composite.
16 is not a term because 16 - 5 = 11 and 16 - 3 = 13 are both prime.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Similar to A130038. Subsequence of A175222.

Cf. A049591, A107986.

Filtered([8..500], k-> IsPrime(k-5) and not IsPrime(k-3) and (k mod 2)=0); # G. C. Greubel, May 21 2019

[n: n in [3..500] | IsPrime(n-5) and not IsPrime(n-3) and (n mod 2) eq 0]; // G. C. Greubel, May 21 2019

N:=100
for n from 8 to N by 2 do
if isprime(n-5) and not isprime(n-3) then print (n);
end if
end do

Select[Range[6, 500, 2], And[PrimeQ[# - 5], ! PrimeQ[# - 3]] &] (* Michael De Vlieger, Jan 10 2018 *)
Select[Range[6, 500, 2], Boole[PrimeQ[# -{5, 3}]] == {1, 0} &] (* Harvey P. Dale, Jan 30 2024 *)

isok(n) = !(n % 2) && isprime(n-5) && !isprime(n-3); \\ Michel Marcus, Jan 09 2018

[n for n in (3..500) if is_prime(n-5) and not is_prime(n-3) and (mod(n, 2)==0)] # G. C. Greubel, May 21 2019

a(n) = A049591(n) + 5 = A107986(n+1) + 3 for all n >= 1.

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

Original entry on oeis.org

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

cp's OEIS Frontend

A052147 a(n) = prime(n) + 2.

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A113935 a(n) = prime(n) + 3.

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A140353 a(n) = prime(n) + 9.

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A175221 a(n) = prime(n) + 4.

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A139049 a(n) = prime(n) + 6.

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Magma

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A175223 a(n) = prime(n) + 7.

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GAP

Magma