A107986 -id:A107986 - 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

A062721 Numbers k such that k is a product of two primes and k-2 is prime.

Original entry on oeis.org

4, 9, 15, 21, 25, 33, 39, 49, 55, 69, 85, 91, 111, 115, 129, 133, 141, 159, 169, 183, 201, 213, 235, 253, 259, 265, 295, 309, 319, 339, 355, 361, 381, 391, 403, 411, 445, 451, 469, 481, 489, 493, 501, 505, 511, 543, 559, 565, 573, 579, 589, 633, 649, 655, 679

Offset: 1

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 14 2001

This sequence is a subsequence of A107986, which only requires k to be composite. The first term in that sequence which is not in this sequence is 45, a number with three prime factors. - Alonso del Arte, May 03 2014

Zak Seidov, Table of n, a(n) for n = 1..10000.

Cf. A006512, A001358, A043326.

Cf. A063637, A046315, A089268.

Select[ Range[ 2, 1500 ], Plus @@ Last@Transpose@FactorInteger[ # ] == 2 && PrimeQ[ # - 2 ] & ]
Select[Range[700], PrimeOmega[#] == 2 && PrimeQ[# - 2]&] (* Harvey P. Dale, Mar 25 2013 *)

{ n=0; for (m=1, 10^9, a=prime(m) + 2; f=factor(a)~; if ((length(f)==1 && f[2, 1]==2) || (length(f)==2 && f[2, 1]==1 && f[2, 2]==1), write("b062721.txt", n++, " ", a); if (n==10000, break)) ) } \\ Harry J. Smith, Aug 09 2009

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.

A241809 Semiprimes sp such that sp+2 is a prime.

Original entry on oeis.org

9, 15, 21, 35, 39, 51, 57, 65, 69, 77, 87, 95, 111, 129, 155, 161, 177, 209, 221, 237, 249, 267, 291, 305, 309, 329, 335, 365, 371, 377, 381, 395, 407, 417, 437, 447, 485, 489, 497, 501, 519, 545, 591, 597, 611, 629, 671, 681, 689, 699, 707, 717, 731, 737, 749

Offset: 1

K. D. Bajpai, Apr 29 2014

			a(2) = 15 = 3*5, which is semiprime and 15+2 = 17 is a prime.
a(6) = 51 = 3*17, which is semiprime and 51+2 = 53 is a prime.

K. D. Bajpai, Table of n, a(n) for n = 1..1370

Cf. A001358, A062721, A063638, A107986.

with(numtheory): A241809:= proc(); if bigomega(x)=2 and isprime(x+2)then  RETURN (x); fi; end: seq(A241809 (), x=1..2000);

A241809={};Do[If[PrimeOmega[n]==2&&PrimeQ[n+2],AppendTo[A241809,n]],{n,1000}];A241809
Select[Prime[Range[200]]-2,PrimeOmega[#]==2&] (* Harvey P. Dale, Aug 06 2015 *)
SequencePosition[Table[Which[PrimeQ[n],1,PrimeOmega[n]==2,2,True,0],{n,800}],{2,,1}][[;;,1]] (* _Harvey P. Dale, Oct 05 2023 *)

for(k=1, 1000, if(bigomega(k)==2 && isprime(k+2), print1(k, ", "))) \\ Colin Barker, May 07 2014

a(n) = A063638(n) - 2.

A164383 Composite numbers of the form 4 + some prime.

Original entry on oeis.org

6, 9, 15, 21, 27, 33, 35, 45, 51, 57, 63, 65, 75, 77, 87, 93, 105, 111, 117, 135, 141, 143, 153, 155, 161, 171, 177, 183, 185, 195, 201, 203, 215, 231, 237, 243, 245, 255, 261, 267, 273, 275, 285, 287, 297, 315, 321, 335, 341, 351, 357, 363, 371, 377, 387, 393

Offset: 1

Juri-Stepan Gerasimov, Aug 14 2009

nonn

			a(1)= 4+2(prime)=6 (composite). a(2)= 4+5(prime)=9 (composite). a(3)=4+11(prime) = 15 (composite).

Cf. A000040, A002808, A107986, A046132.

Select[4+Prime[Range[100]],CompositeQ] (* Harvey P. Dale, Oct 24 2017 *)

Edited, entries checked, by R. J. Mathar, Aug 20 2009

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

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A062721 Numbers k such that k is a product of two primes and k-2 is prime.

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

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A241809 Semiprimes sp such that sp+2 is a prime.

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A164383 Composite numbers of the form 4 + some prime.

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