A137847 -id:A137847 - cp's OEIS frontend

A064425 Gaps between where primes occur in A064413.

3, 5, 4, 6, 8, 5, 4, 6, 14, 4, 6, 7, 7, 8, 11, 7, 8, 13, 6, 4, 13, 9, 7, 15, 7, 8, 6, 4, 9, 20, 17, 6, 5, 15, 8, 10, 8, 9, 14, 8, 8, 19, 8, 6, 4, 20, 19, 10, 8, 6, 14, 4, 12, 13, 14, 9, 7, 13, 10, 9, 8, 24, 6, 12, 7, 23, 10, 16, 9, 6, 11, 18, 8, 17, 6, 6, 20, 10, 15

Offset: 1

N. J. A. Sloane, Oct 01 2001

nonn

T. D. Noe, Table of n, a(n) for n=1..1000
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, arXiv:math/0204011 [math.NT], 2002.
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446.
Index entries for sequences related to EKG sequence

Cf. A064413. First differences of A064955 and also of A064423.

Cf. A137847.

terms = 80;
ekg[s_] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
EKG = Nest[ekg, {2, 4}, 12 terms];
fp[n_] := FirstPosition[EKG, Prime[n]][[1]];
Array[fp, terms] // Differences (* Jean-François Alcover, Sep 02 2018, after Robert G. Wilson v in A064413 *)

A387089 Smallest number missing in the sequence A386482 after n terms.

Original entry on oeis.org

2, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23

Offset: 1

Rémy Sigrist, Aug 16 2025

nonn

			The first terms, alongside the first terms of A386482, are:
  n   a(n)  A386482(n)
  --  ----  ----------
   1     2           1
   2     3           2
   3     3           4
   4     3           6
   5     5           3
   6     5           9
   7     5          12
   8     5          10
   9     5           8
  10     5          14
  11     5           7
  12     5          21
  13     5          18
  14     5          16
  15     5          20
  16     5          15
  17    11           5

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A137847, A386482.

PARI
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A064425 Gaps between where primes occur in A064413.

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