A049232 -id:A049232 - cp's OEIS frontend

A091880 A049232 indexed by A000040.

1, 4, 9, 14, 15, 18, 21, 22, 25, 36, 39, 40, 48, 53, 59, 65, 67, 70, 72, 73, 74, 82, 85, 88, 99, 101, 110, 114, 122, 125, 127, 129, 130, 137, 143, 146, 147, 155, 158, 168, 174, 177, 180, 181, 188, 194, 198, 200, 202, 204, 213, 216, 219, 220, 224, 226, 229, 235

Offset: 1

Ray Chandler, Feb 15 2004

The asymptotic density of this sequence is 1 - 2 * Product_{p prime} (1-1/(p*(p-1))) = 1 - 2 * A005596 = 0.252088... - Amiram Eldar, Feb 28 2021

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000040, A005596, A049232.

Select[Range[100], ! SquareFreeQ[Prime[ # ] + 2] &] (* Zak Seidov, Oct 28 2008 *)

a(n) = k such that A000040(k) = A049232(n).

A089176 Duplicate of A049232.

Original entry on oeis.org

2, 7, 23, 43, 47, 61, 73, 79, 97, 151, 167, 173, 223, 241, 277, 313, 331, 349, 359, 367

Offset: 1

dead

A049229 Primes p such that p-2 is not squarefree.

Original entry on oeis.org

11, 29, 47, 83, 101, 127, 137, 149, 173, 191, 227, 263, 277, 281, 317, 353, 389, 443, 461, 479, 509, 541, 569, 577, 587, 607, 641, 659, 677, 727, 821, 827, 839, 857, 877, 911, 929, 947, 977, 983, 1019, 1031, 1091, 1109, 1129, 1163, 1181, 1217, 1277, 1289

Offset: 1

Labos Elemer

nonn

This sequence is infinite and its relative density in the sequence of the primes is equal to 1 - 2 * Product_{p prime} (1-1/(p*(p-1))) = 1 - 2 * A005596 = 0.252088... - Amiram Eldar, Feb 27 2021

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

Cf. A005596, A013929, A049231, A049232.

Select[Prime[Range[2,300]],!SquareFreeQ[#-2]&] (* Harvey P. Dale, Nov 14 2012 *)

isok(p) = (p>2) && isprime(p) && !issquarefree(p-2); \\ Michel Marcus, May 14 2018

A090870 a(n) is the smallest m such that d(m+k-1) = 2k for k = 1, ..., n where d(t)= prime(t+1) - prime(t) (differences of consecutive primes in arithmetic progression).

Original entry on oeis.org

2, 3, 7, 69, 1642, 12073, 12073, 6496152, 118033638, 5575956036, 165534366186, 3265469041280, 14779996741980, 5701362336480884

Offset: 1

Farideh Firoozbakht, Dec 11 2003

Is this sequence infinite?

			a(8) = 6496152 because prime(6496152) = 113575727 and 113575727, 113575729, 113575733, 113575739, 113575747, 113575757, 113575769, 113575783, and 113575799 are nine consecutive primes with differences respectively 2, 4, 6, 8, 10, 12, 14, 16.

Cf. A016045, A049232.

a[n_] := (For[m=1, !Sum[(d[m+k-1]-2k)^2, {k, n}]==0, m++ ];m); Do[Print[a[n]], {n, 8}]

a(n) = primePi(A016045(n)).

Extended and edited by T. D. Noe, May 23 2011

a(11)-a(14) from Amiram Eldar, Sep 06 2024

cp's OEIS Frontend

A091880 A049232 indexed by A000040.

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A089176 Duplicate of A049232.

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A049229 Primes p such that p-2 is not squarefree.

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A090870 a(n) is the smallest m such that d(m+k-1) = 2k for k = 1, ..., n where d(t)= prime(t+1) - prime(t) (differences of consecutive primes in arithmetic progression).

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