A089527 -id:A089527 - cp's OEIS frontend

A088119 Sequence of primes p(n) such that 2p(n)+3, 2p(n+1)+3, 2*p(n+2)+3 are consecutive primes, where p(i) denotes the i-th prime.

193, 223, 1607, 15733, 39877, 63647, 65407, 68207, 72673, 84299, 89977, 96787, 99137, 102533, 103687, 115837, 127807, 143567, 150373, 191999, 204793, 257867, 324217, 344957, 375253, 412033, 427433, 491149, 551717, 595117, 642527, 646897

Offset: 1

Pierre CAMI, Nov 02 2003

nonn

			p(44) = 193, 2*193 + 3 = 389 = p(77);
p(45) = 197, 2*197 + 3 = 397 = p(78);
p(46) = 199, 2*199 + 3 = 401 = p(79).

Robert Israel, Table of n, a(n) for n = 1..2000

Subsequence of A089527.

Cf. A088066, A089450, A089525.

r:= 1: q:= 2: p:= 3: count:= 0:
while count < 100 do
  r:= q; q:= p; p:= nextprime(p);
  if isprime(2*r+3) and nextprime(2*r+3)=2*q+3 and nextprime(2*q+3)=2*p+3 then
    count:= count+1;
    A[count]:= r;
  fi
od:seq(A[i],i=1..100); # Robert Israel, Jul 01 2018

a(n) = A000040(A088066(n)).

More terms from Ray Chandler, Nov 03 2003

Offset corrected by Robert Israel, Jul 01 2018

A089526 Numbers n such that 2p(n)+3 and 2p(n+1)+3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

3, 7, 14, 33, 44, 45, 48, 49, 70, 75, 90, 174, 186, 213, 225, 246, 253, 254, 447, 505, 524, 531, 589, 592, 625, 665, 745, 766, 806, 866, 868, 989, 1047, 1084, 1091, 1105, 1131, 1191, 1202, 1228, 1257, 1280, 1333, 1395, 1410, 1429, 1495, 1512, 1550, 1643, 1651

Offset: 1

Ray Chandler, Nov 07 2003

nonn

			p(3)=5, 2*5+3=13=p(6)
p(4)=7, 2*7+3=17=p(7)

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Subsequence of A089530. Cf. A089527, A089528, A089529.

cpQ[n_]:=Module[{p=2Prime[n]+3},PrimeQ[p]&&NextPrime[p]==2Prime[n+1]+3]; Select[Range[1700],cpQ] (* Harvey P. Dale, Nov 29 2014 *)

A089528 Primes p of the form 2prime(k) + 3 such that 2prime(k+1) + 3 is the next prime after p.

Original entry on oeis.org

13, 37, 89, 277, 389, 397, 449, 457, 701, 761, 929, 2069, 2221, 2609, 2857, 3121, 3217, 3221, 6329, 7229, 7537, 7649, 8581, 8677, 9277, 9941, 11317, 11681, 12401, 13421, 13469, 15649, 16729, 17401, 17497, 17729, 18257, 19289, 19489, 19937, 20509

Offset: 1

Ray Chandler, Nov 07 2003

nonn

			p(3)=5, 2*5 + 3 = 13 = p(6);
p(4)=7, 2*7 + 3 = 17 = p(7).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Subsequence of A089531.

Cf. A089526, A089527, A089529.

Select[Partition[2#+3&/@Prime[Range[2500]],2,1],AllTrue[#,PrimeQ] && NextPrime[ #[[1]]]==#[[2]]&][[All,1]] (* Harvey P. Dale, Dec 14 2021 *)

forprime(p=2,10500,my(p23=2*p+3);if(isprime(p23),my(pp=2*nextprime(p+1)+3);if(isprime(pp)&&pp==nextprime(p23+1),print1(p23,", ")))) \\ Hugo Pfoertner, Aug 04 2021

a(n) = 2*A089527(n) + 3 = 2*A000040(A089526(n)) + 3 = A000040(A089529(n)).

Offset changed to 1 by Jinyuan Wang, Aug 04 2021

A089529 A089528 indexed by A000040.

Original entry on oeis.org

6, 12, 24, 59, 77, 78, 87, 88, 126, 135, 158, 312, 331, 379, 415, 445, 455, 456, 824, 924, 955, 971, 1069, 1080, 1148, 1226, 1368, 1402, 1480, 1592, 1597, 1826, 1934, 2002, 2014, 2035, 2093, 2187, 2212, 2254, 2315, 2353, 2461, 2587, 2619, 2653, 2766, 2792

Offset: 1

Ray Chandler, Nov 07 2003

nonn

			prime(3)=5, 2*5 + 3 = 13 = prime(6);
prime(4)=7, 2*7 + 3 = 17 = prime(7).

Subsequence of A089532.

Cf. A089526, A089527, A089528.

a(n) = k such that A089528(n) = A000040(k).

a(n) = A000720(A089528(n)). - Michel Marcus, Aug 04 2021

Offset changed to 1 by Jinyuan Wang, Aug 04 2021

cp's OEIS Frontend

A088119 Sequence of primes p(n) such that 2*p(n)+3, 2*p(n+1)+3, 2*p(n+2)+3 are consecutive primes, where p(i) denotes the i-th prime.

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A089526 Numbers n such that 2*p(n)+3 and 2*p(n+1)+3 are consecutive primes, where p(i) denotes the i-th prime.

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A089528 Primes p of the form 2*prime(k) + 3 such that 2*prime(k+1) + 3 is the next prime after p.

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A089529 A089528 indexed by A000040.

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A088119 Sequence of primes p(n) such that 2p(n)+3, 2p(n+1)+3, 2*p(n+2)+3 are consecutive primes, where p(i) denotes the i-th prime.

A089526 Numbers n such that 2p(n)+3 and 2p(n+1)+3 are consecutive primes, where p(i) denotes the i-th prime.

A089528 Primes p of the form 2prime(k) + 3 such that 2prime(k+1) + 3 is the next prime after p.