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

Author

Gus Wiseman, Dec 10 2024

Keywords

• nonn

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

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

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.

Programs

Mathematica

Select[Range[100],Prime[#]+2==Prime[#+1]&&!SquareFreeQ[Prime[#]+1]&]
PrimePi/@Select[Partition[Prime[Range[500]],2,1],#[[2]]-#[[1]]==2&&!SquareFreeQ[Mean[#]]&][[;;,1]] (* Harvey P. Dale, Jul 13 2025 *)

Formula

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