

A307632


Index of first occurrence of nth prime in A307720.


6



3, 5, 47, 53, 1374, 1386, 3738, 3756, 6680, 6704, 84626, 84658, 89480, 89522, 91832, 91880, 173092, 173152, 192882, 192950, 524587, 524661, 865301, 865385, 876543, 876641, 890479, 890583, 904273, 904383, 918859, 918987, 1628979, 1629117, 1647107, 1647257, 1666775
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OFFSET

1,1


COMMENTS

It follows from the definition of A307720 that if p = kth prime, k>1 and k odd, and q = (k+1)st prime, then the first time p appears in the sequence is at the start of a subsequence (p,1) [(p1)/2 times], p, (1,q) [{q+1)/2 times].
For example, the fifth prime 11 first appears in A307720 at step 1374 at the start of the subsequence 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13.
So q appears p+1 steps after p, which explains why the terms of the present sequence appear in pairs.
In fact it appears that one can make a much stronger statement about what happens immediately after the first occurrence of p. Look at the terms in A307720 following the first 11 at step 1374. It may be that the next O(p^2) terms are forced.


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..1229 [Taken from Rémy Sigrist's bfile for A307630. First 132 terms from Hans Havermann.]


CROSSREFS

Cf. A307720, A307630, A307631.
First differences = A348773.
Sequence in context: A062633 A240559 A352088 * A227743 A335752 A343768
Adjacent sequences: A307629 A307630 A307631 * A307633 A307634 A307635


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 26 2019


EXTENSIONS

More terms from Hans Havermann, Apr 26 2019


STATUS

approved



