A084106 Larger difference (r-q or q-p) associated with A084105.

2, 6, 14, 10, 12, 18, 22, 24, 28, 30, 34, 42, 52, 54, 58, 60, 70, 82, 90, 100, 118, 132, 136, 148, 150, 168, 178, 196, 208, 214, 220, 234, 250, 288, 310, 318, 330, 360, 366, 384, 390, 402, 408, 414, 454, 462, 516, 588, 598, 610, 648, 706, 712, 736, 754, 756, 760

Offset

1,1

Comments

Differences > a(46) = 462 require search beyond 10^12. - Hugo Pfoertner, Sep 02 2020

Searched range through 10^13. - Hugo Pfoertner, Sep 17 2020

Links

Table of n, a(n) for n=1..57.

Example

a(5)=12 because the larger difference between A084105(5)=199 and its prime neighbors 197 and 211 is 211-199=12.
a(51)=648 corresponds to the gaps between the 3 consecutive primes 9787731507761, 9787731508409, 9787731508411. - Hugo Pfoertner, Sep 19 2020

Prog

(PARI) default(realprecision, 20); default(primelimit, 436270000); { apt(m)= local(dl, dr, q, qm); qm=1.0; for(n=2, m, dl=prime(n)-prime(n-1); dr=prime(n+1)-prime(n); q=min(dl, dr)/max(dl, dr)+0.; if(q<qm, qm=q; print(dl" "dr" "max(dl, dr)" "q" "prime(n)" "n-1))); }
(PARI) a084106(limit)={my(p1=2, p2=3, q=0); forprime(k=5, limit, my(r=max((p2-p1)/(k-p2), (k-p2)/(p2-p1))); if(r>q, q=r; print1(max(p2-p1, k-p2), ", ")); p1=p2; p2=k)};
a084106(10^9) \\ Hugo Pfoertner, Sep 02 2020

Crossrefs

Cf. A002386, A084105, A337489.

Sequence in context: A091719 A058054 A054588 * A295987 A263691 A160657

Adjacent sequences: A084103 A084104 A084105 * A084107 A084108 A084109

Keyword

nonn

Author

Hugo Pfoertner, May 29 2003

Extensions

More terms from Don Reble and Jason Earls, May 29 2003

a(36)-a(46) from Hugo Pfoertner, Sep 02 2020

a(47)-a(51) from Hugo Pfoertner, Sep 17 2020

a(52)-a(57) from Martin Ehrenstein, Aug 07 2021

Status

approved