A054810 -id:A054810

Search: a054810 -id:a054810

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A054809

Second term of strong prime 5-tuples: p(m)-p(m-1) > p(m+1)-p(m) > p(m+2)-p(m+1) > p(m+3)-p(m+2).

+10
3

1657, 1777, 1847, 1861, 1987, 2371, 2459, 2503, 2521, 3433, 3449, 4201, 4507, 5261, 5407, 5431, 6029, 6637, 7229, 7283, 7741, 7867, 7919, 8147, 8501, 9587, 9601, 11027, 11369, 11579, 11821, 12391, 13859, 14813, 15121, 15527, 16033, 16301

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Initial member of pairs of consecutive primes in A054805 (second of quadruples): The first 10^4 terms of that sequence yield over 2000 terms of this sequence. - M. F. Hasler, Oct 27 2018

LINKS

M. F. Hasler, Table of n, a(n) for n = 1..2000

FORMULA

a(n) = nextprime(A054808(n)) = prevprime(A054810(n)), nextprime = A151800, prevprime = A151799; A054809 = {m = A054805(n) | nextprime(m) = A054805(n+1)}. - M. F. Hasler, Oct 27 2018

MATHEMATICA

spqQ[n_]:=Module[{difs=Differences[n]}, difs[[1]]>difs[[2]]> difs[[3]]> difs[[4]]]; Transpose[Select[Partition[Prime[ Range[2000]], 5, 1], spqQ]][[2]] (* Harvey P. Dale, May 06 2012 *)

CROSSREFS

Cf. A051634, A051635; A054800 .. A054803: members of balanced prime quadruples (= 4 consecutive primes in arithmetic progression); A054804 .. A054818: members of strong prime 4-tuples, 5-tuples, 6-tuples; A054819 .. A054840: members of weak prime 4-tuples, ..., 7-tuples.

KEYWORD

nonn

AUTHOR

Henry Bottomley, Apr 10 2000

EXTENSIONS

Corrected by Harvey P. Dale, May 06 2012

Edited and offset corrected to 1 by M. F. Hasler, Oct 27 2018

STATUS

approved

A054811

Fourth term of strong prime quintets: p(m-2)-p(m-3) > p(m-1)-p(m-2) > p(m)-p(m-1) > p(m+1)-p(m).

+10
2

1667, 1787, 1867, 1871, 1997, 2381, 2473, 2531, 2539, 3457, 3461, 4217, 4517, 5279, 5417, 5441, 6043, 6659, 7243, 7307, 7757, 7877, 7933, 8167, 8521, 9613, 9619, 11057, 11393, 11593, 11831, 12409, 13877, 14827, 15137, 15551, 16061, 16333

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

First member of pairs of consecutive primes in A054807 (4th of strong prime quartets). - M. F. Hasler, Oct 27 2018

LINKS

M. F. Hasler, Table of n, a(n) for n = 1..2000, Oct 27 2018

FORMULA

a(n) = nextprime(A054810(n)) = prevprime(A054812(n)), nextprime = A151800, prevprime = A151799; A054811 = {m = A054807(n) | nextprime(m) = A054807(n+1)}. - M. F. Hasler, Oct 27 2018

CROSSREFS

Cf. A051634, A051635; A054800 .. A054803: members of balanced prime quartets (= 4 consecutive primes in arithmetic progression); A054804 .. A054818: members of strong prime quartets, quintets, sextets; A054819 .. A054840: members of weak prime quartets, quintets, sextets, septets.

KEYWORD

nonn

AUTHOR

Henry Bottomley, Apr 10 2000

STATUS

approved

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