A089450 -id:A089450 - cp's OEIS frontend

A089525 A089450 indexed by A000040.

77, 87, 455, 3386, 7811, 11926, 12233, 12705, 13448, 15382, 16338, 17462, 17844, 18387, 18580, 20577, 22492, 25001, 26060, 32604, 34578, 42718, 52713, 55807, 60272, 65730, 67963, 77232, 85964, 92239, 98963, 99587, 100386, 102163, 103689

Offset: 1

Ray Chandler, Nov 07 2003

nonn

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

Subsequence of A089529.

Cf. A088066, A088119, A089450.

a(n) = k such that A089450(n) = A000040(k).

a(n) = A000720(A089450(n)). - Michel Marcus, Aug 04 2021

Offset changed to 1 by Jinyuan Wang, Aug 04 2021

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.

Original entry on oeis.org

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

A089492 Sequence of primes 2p(k) + 3 such that 2p(k) + 3, 2p(k+1) + 3, 2p(k+2) + 3, 2*p(k+3) + 3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

1552237, 4315469, 8774137, 9629197, 10048081, 10875149, 11469389, 14498741, 18280861, 18789629, 19309957, 19309981, 25386029, 27265457, 28398641, 29697029, 31298269, 31355297, 36792901, 47318969, 47487889, 55449689

Offset: 1

Ray Chandler, Nov 04 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 A089450.

Cf. A089007, A089009, A089524.

a089492(limit)={my(pv=[2,3,5,0],v3=[3,3,3,3],ks(k)=2*k+3);forprime(p=7,limit,pv[4]=p;if(vecsum(isprime(2*pv+v3))==4&&primepi(ks(pv[4]))-primepi(ks(pv[1]))==3,print1(ks(pv[1]),", "));pv[1]=pv[2];pv[2]=pv[3];pv[3]=pv[4])};
a089492(30000000) \\ Hugo Pfoertner, Aug 06 2021

a(n) = 2*A089007(n) + 3 = 2*A000040(A089009(n)) + 3 = A000040(A089524(n)).

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

cp's OEIS Frontend

A089525 A089450 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.

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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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Author

Keywords

Examples

Crossrefs

Extensions

A089492 Sequence of primes 2p(k) + 3 such that 2p(k) + 3, 2p(k+1) + 3, 2p(k+2) + 3, 2*p(k+3) + 3 are consecutive primes, where p(i) denotes the i-th prime.

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PARI

Formula

Extensions

cp's OEIS Frontend

A089525 A089450 indexed by A000040.

Views

Author

Keywords

Examples

Crossrefs

Formula

Extensions

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.

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Author

Keywords

Examples

Crossrefs

Extensions

A089492 Sequence of primes 2*p(k) + 3 such that 2*p(k) + 3, 2*p(k+1) + 3, 2*p(k+2) + 3, 2*p(k+3) + 3 are consecutive primes, where p(i) denotes the i-th prime.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

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.

A089492 Sequence of primes 2p(k) + 3 such that 2p(k) + 3, 2p(k+1) + 3, 2p(k+2) + 3, 2*p(k+3) + 3 are consecutive primes, where p(i) denotes the i-th prime.