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A054342 First occurrence of distances of equidistant lonely primes. Each equidistant prime is at the same distance (or has the same gap) from the preceding prime and the next prime. 8
5, 53, 211, 20201, 16787, 69623, 255803, 247141, 3565979, 6314447, 4911311, 12012743, 23346809, 43607429, 34346287, 36598607, 51042053, 460475569, 652576429, 742585297, 530324449, 807620777, 2988119339, 12447231899, 383204683, 4470608101, 5007182863, 71015248091, 5558570491, 88526967847, 65997364621, 48287689717, 57484162331, 50284155289, 178796541817, 264860525507, 978720895253, 472446412421, 374787490919 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or, least balanced primes: starting with 2nd term, 53, the smallest prime such that the distances to the next smallest and next largest primes are both equal to 6n.

The distances corresponding to the above terms are 2,6,12,18,24...192,198,204,210,218,224.

LINKS

Table of n, a(n) for n=1..39.

EXAMPLE

211 is an equidistant lonely prime with distance 12. This is the first occurrence of the distance 12, thus 211 is in the sequence.

20201 is a least balanced prime because it is the third term in the sequence and is separated from both the next lower and next higher primes by 3 x 6 = 18.

Here is the beginning of the table of equidistant lonely primes.

Equivalent to 3 consecutive primes in arithmetic progression.

* indicates a maximal gap. This table gives rise to A058867, A058868 and the present sequence.

Gap First occurrence

--- ----------------

2* 5

6* 53

12* 211

18 20201

24* 16787

30* 69623

36 255803

42* 247141

48* 3565979

54 6314447

60* 4911311

66* 12012743

72* 23346809

78 43607429

84* 34346287

90* 36598607

96* 51042053

102 460475569

108 652576429

CROSSREFS

Cf. A058867, A058868, A006562, A103709.

Sequence in context: A267543 A058867 A058869 * A216533 A152473 A242906

Adjacent sequences:  A054339 A054340 A054341 * A054343 A054344 A054345

KEYWORD

nonn

AUTHOR

Harvey P. Dale, May 06 2000

EXTENSIONS

More terms from Jud McCranie, Jun 13 2000

Further terms from Harvey Dubner (harvey(AT)dubner.com), Sep 11 2004

Entry revised by N. J. A. Sloane, Jul 23 2006

4 further terms from Walter Neumann (neumann(AT)math.columbia.edu), Aug 14 2006

STATUS

approved

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Last modified October 21 11:34 EDT 2019. Contains 328296 sequences. (Running on oeis4.)