A089525 -id:A089525 - 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

A088066 Numbers 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.

Original entry on oeis.org

44, 48, 253, 1834, 4193, 6380, 6532, 6788, 7187, 8216, 8711, 9318, 9519, 9817, 9908, 10947, 11971, 13308, 13880, 17326, 18366, 22664, 27938, 29576, 31931, 34773, 35960, 40853, 45454, 48736, 52256, 52586, 53010, 53956, 54758, 59618, 62178

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)

Subsequence of A089526.

Cf. A088119, A089450, A089525.

More terms from Ray Chandler, Nov 03 2003

A089450 Sequence of primes 2p(k) + 3 such that 2p(k) + 3, 2p(k+1) + 3, 2p(k+2) + 3 are consecutive primes, where p(i) denotes the i-th prime. Sequence terms are 2*p(k) + 3.

Original entry on oeis.org

389, 449, 3217, 31469, 79757, 127297, 130817, 136417, 145349, 168601, 179957, 193577, 198277, 205069, 207377, 231677, 255617, 287137, 300749, 384001, 409589, 515737, 648437, 689917, 750509, 824069, 854869, 982301, 1103437, 1190237

Offset: 1

Ray Chandler, Nov 03 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).

Subsequence of A089528.

Cf. A088066, A088119, A089525.

cpQ[n_]:=Module[{p1=2n+3,p2=2NextPrime[n]+3,p3=2NextPrime[n,2]+3,pr = PrimePi[ 2n+3]},{p1,p2,p3}==Prime[Range[pr,pr+2]]]; 2#+3&/@ Select[ Prime[ Range[50000]],cpQ] (* Harvey P. Dale, Sep 24 2019 *)

a(n) = 2*A088119(n) + 3 = 2*A000040(A088066(n)) + 3 = A000040(A089525(n)).

Definition clarified by Harvey P. Dale, Sep 24 2019

Offset changed to 1 by Jinyuan Wang, Aug 04 2021

A089524 A089492 indexed by A000040.

Original entry on oeis.org

117814, 303839, 588398, 641658, 667591, 718808, 755409, 940389, 1168122, 1198507, 1229482, 1229483, 1588488, 1698574, 1764688, 1840175, 1933195, 1936524, 2249818, 2849725, 2859255, 3307463, 3363452, 3414415, 3481752

Offset: 1

Ray Chandler, Nov 07 2003

nonn

			p(62178)=776117, 2*776117 + 3 = 1552237 = p(117814);
p(62179)=776119, 2*776119 + 3 = 1552241 = p(117815);
p(62180)=776137, 2*776137 + 3 = 1552277 = p(117816);
p(62181)=776143, 2*776143 + 3 = 1552289 = p(117817).

Subsequence of A089525.

Cf. A089007, A089009, A089492.

a(n) = k such that A089492(n) = A000040(k).

a(n) = A000720(A089492(n)). - Michel Marcus, Aug 06 2021

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

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.

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A088066 Numbers 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.

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A089450 Sequence of primes 2p(k) + 3 such that 2p(k) + 3, 2p(k+1) + 3, 2p(k+2) + 3 are consecutive primes, where p(i) denotes the i-th prime. Sequence terms are 2*p(k) + 3.

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A089524 A089492 indexed by A000040.

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Author

Keywords

Examples

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Extensions

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Formula

Extensions

A088066 Numbers 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.

Views

Author

Keywords

Examples

Crossrefs

Extensions

A089450 Sequence of primes 2*p(k) + 3 such that 2*p(k) + 3, 2*p(k+1) + 3, 2*p(k+2) + 3 are consecutive primes, where p(i) denotes the i-th prime. Sequence terms are 2*p(k) + 3.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions

A089524 A089492 indexed by A000040.

Views

Author

Keywords

Examples

Crossrefs

Formula

Extensions

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.

A088066 Numbers 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.

A089450 Sequence of primes 2p(k) + 3 such that 2p(k) + 3, 2p(k+1) + 3, 2p(k+2) + 3 are consecutive primes, where p(i) denotes the i-th prime. Sequence terms are 2*p(k) + 3.