Alan Worley - cp's OEIS frontend

User: Alan Worley

Alan Worley has authored 2 sequences.

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

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

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

			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.

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.

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

Cf. A133697.

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

a(15) from Giovanni Resta, Apr 19 2016

A158940 First primes followed by sequences of exactly n monotonic decreasing prime gaps.

Original entry on oeis.org

2, 7, 31, 1637, 1831, 74653, 322171, 5051309, 11938793, 245333213, 245333159, 130272314561, 1273135176799, 23840790158827

Offset: 1

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

a(15) > 1.3*10^14. - Giovanni Resta, Apr 19 2016

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

			a(4)=1637 is the first prime to be followed by n=4 monotonic decreasing prime gaps: 20,6,4,2.
a(13)=1273135176799 is the first prime to be followed by n=13 monotonic decreasing prime gaps: 72,60,46,44,42,36,34,24,12,8,6,4,2.

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

Cf. A158939 (monotonic increasing prime gaps)

a(14) from Giovanni Resta, Apr 19 2016

cp's OEIS Frontend

User: Alan Worley

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

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