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A201074 Initial primes in prime quintuplets (p, p+2, p+6, p+8, p+12) preceding the maximal gaps in A201073. 3
5, 11, 101, 1481, 22271, 55331, 536441, 661091, 1461401, 1615841, 5527001, 11086841, 35240321, 53266391, 72610121, 92202821, 117458981, 196091171, 636118781, 975348161, 1156096301, 1277816921, 1347962381, 2195593481, 3128295551 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime quintuplets (p, p+2, p+6, p+8, p+12) are one of the two types of densest permissible constellations of 5 primes. Maximal gaps between quintuplets of this type are listed in A201073; see more comments there.

REFERENCES

Hardy, G. H. and Littlewood, J. E. "Some Problems of 'Partitio Numerorum.' III. On the Expression of a Number as a Sum of Primes." Acta Math. 44, 1-70, 1923.

LINKS

Alexei Kourbatov, Table of n, a(n) for n = 1..64

Tony Forbes, Prime k-tuplets

Alexei Kourbatov, Maximal gaps between prime quintuplets (graphs/data up to 10^15)

Eric W. Weisstein, k-Tuple Conjecture

EXAMPLE

The initial four gaps of 6, 90, 1380, 14580 (starting at p=5, 11, 101, 1481) form an increasing sequence of records. Therefore a(1)=5, a(2)=11, a(3)=101, and a(4)=1481. The next gap is smaller, so a new term is not added.

CROSSREFS

Cf. A022006 (prime quintuplets p, p+2, p+6, p+8, p+12), A201073, A233432.

Sequence in context: A088268 A030085 A022006 * A056111 A090160 A062652

Adjacent sequences:  A201071 A201072 A201073 * A201075 A201076 A201077

KEYWORD

nonn

AUTHOR

Alexei Kourbatov, Nov 26 2011

STATUS

approved

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Last modified October 25 15:08 EDT 2014. Contains 248556 sequences.