A378620 Lesser prime index of twin primes with nonsquarefree mean.

2, 5, 7, 17, 20, 28, 35, 41, 43, 45, 49, 52, 57, 64, 69, 81, 83, 98, 109, 120, 140, 144, 152, 171, 173, 176, 178, 182, 190, 206, 215, 225, 230, 236, 253, 256, 262, 277, 286, 294, 296, 302, 307, 315, 318, 323, 336, 346, 373, 377, 390, 395, 405, 428, 430, 444

Offset

1,1

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

This is a subset of A029707 (twin prime indices). The other twin primes are A068361, so A029707 is the disjoint union of A068361 and A378620.

Links

Table of n, a(n) for n=1..56.

Formula

prime(a(n)) = A061368(n).

Mathematica

Select[Range[100], Prime[#]+2==Prime[#+1]&&!SquareFreeQ[Prime[#]+1]&]

Crossrefs

The lesser of twin primes is A001359, index A029707 (complement A049579).

The greater of twin primes is A006512, index A107770 (complement appears to be A168543).

A subset of A029707 (twin prime lesser indices).

Prime indices of the primes listed by A061368.

Indices of twin primes with squarefree mean are A068361.

A000040 lists the primes, differences A001223, (run-lengths A333254, A373821).

A005117 lists the squarefree numbers, differences A076259.

A006562 finds balanced primes.

A013929 lists the nonsquarefree numbers, differences A078147.

A014574 is the intersection of A006093 and A008864.

A038664 finds the first position of a prime gap of 2n.

A046933 counts composite numbers between primes.

A120327 gives the least nonsquarefree number >= n.

Cf. A007674, A072284, A068360.

Cf. A057627, A061398, A061399, A067535, A070321, A071403, A112925.

Cf. A000720, A025584, A067774, A122535, A155752, A179067.

Sequence in context: A105895 A238699 A068360 * A110254 A019084 A278487

Adjacent sequences: A378616 A378617 A378618 * A378626 A378629 A378630

Keyword

nonn,new

Author

Gus Wiseman, Dec 10 2024

Status

approved