A373817 Positions of terms > 1 in the run-lengths of the first differences of the odd primes.

2, 14, 34, 36, 42, 49, 66, 94, 98, 100, 107, 117, 147, 150, 169, 171, 177, 181, 199, 219, 250, 268, 315, 333, 361, 392, 398, 435, 477, 488, 520, 565, 570, 585, 592, 595, 628, 642, 660, 666, 688, 715, 744, 765, 772, 778, 829, 842, 897, 906, 931, 932, 961, 1025

Offset

1,1

Comments

Positions of terms > 1 in A333254. In other words, the a(n)-th run of differences of odd primes has length > 1.

Links

Table of n, a(n) for n=1..54.

Example

Primes 54 to 57 are {251, 257, 263, 269}, with differences (6,6,6). This is the 49th run, and the first of length > 2.

Mathematica

Join@@Position[Length /@ Split[Differences[Select[Range[1000], PrimeQ]]] // Most, x_Integer?(#>1&)]

Crossrefs

Positions of adjacent equal prime gaps are A064113.

Positions of adjacent unequal prime gaps are A333214.

Positions of terms > 1 in A333254, run-lengths A373821, firsts A335406.

A000040 lists the primes, differences A001223.

A027833 gives antirun lengths of odd primes, run-lengths A373820.

A046933 counts composite numbers between primes.

A065855 counts composite numbers up to n.

A071148 gives partial sums of odd primes.

Cf. A006560, A006562, A029707, A031217, A037201, A038664, A069010, A073051, A089180, A251092.

Sequence in context: A378259 A368628 A282036 * A050591 A073535 A225292

Adjacent sequences: A373814 A373815 A373816 * A373818 A373819 A373820

Keyword

nonn

Author

Gus Wiseman, Jun 23 2024

Status

approved