A158939 First primes followed by sequences of exactly n monotonic increasing prime gaps.

3, 2, 17, 347, 2903, 15373, 128981, 1319407, 17797517, 94097537, 6927837557, 48486712783, 968068681511, 1472840004017, 129001208165717

Offset

1,1

Comments

For n > 1, a(n) is the prime preceding A229832(n-1). [Follows from the definitions] - Chris Boyd, Mar 28 2015

Banks, Freiberg, & Turnage-Butterbaugh show that a(n) exists for each n. - Charles R Greathouse IV, Jun 30 2022

Links

Table of n, a(n) for n=1..15.

William D. Banks, Tristan Freiberg, and Caroline L. Turnage-Butterbaugh, Consecutive primes in tuples (2013), arXiv:1311.7003 [math.NT].

Carlos Rivera, Puzzle 11. Distinct, Increasing & Decreasing Gaps, The Prime Puzzles and Problems Connection.

Example

a(8)=1319407 is the first prime to be followed by n=8 monotonic increasing prime gaps: 4,8,10,14,16,18,32,34.
a(14)=1472840004017 is the first prime to be followed by n=14 monotonic increasing prime gaps: 2,4,6,8,10,12,14,28,30,38,48,64,66,74.

Prog

(PARI) is(p, k, g=0)=my(q=nextprime(p+1)); if(g>=q-p, 0, if(k>1, is(q, k-1, q-p), q-p>=nextprime(q+1)-q))
a(n)=forprime(p=2, , if(is(p, n), return(p))) \\ Charles R Greathouse IV, Nov 02 2012

Crossrefs

Cf. A158940 (monotonic decreasing prime gaps), A229832.

Cf. A133697.

Sequence in context: A342140 A126354 A361084 * A173795 A249769 A026345

Adjacent sequences: A158936 A158937 A158938 * A158940 A158941 A158942

Keyword

more,nonn

Author

Alan Worley (aw(AT)xiboo.co.uk), Mar 31 2009

Extensions

a(15) from Giovanni Resta, Apr 19 2016

Status

approved