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Revision History for A118469 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing all changes.
Triangle read by rows: a(n,m) = If(n = 1, then 1, else Prime(n) - 1 + Sum_{k=n..m} (Prime(k + 1) - Prime(k))/2 ).
(history; published version)
#5 by Andrey Zabolotskiy at Fri Dec 29 12:52:12 EST 2023
STATUS

editing

approved

#4 by Andrey Zabolotskiy at Fri Dec 29 12:52:08 EST 2023
NAME

Triangle read by rows: a(n,m) = If(n = 1, then 1, else Prime(n) - 1 + Sum_{k=n..m} (Prime(k + 1) - Prime(k))/2 ).

STATUS

approved

editing

#3 by Charles R Greathouse IV at Wed Mar 12 16:36:52 EDT 2014
AUTHOR

_Roger L. Bagula_, May 04 2006

Discussion
Wed Mar 12
16:36
OEIS Server: https://oeis.org/edit/global/2126
#2 by Russ Cox at Fri Mar 30 18:49:15 EDT 2012
AUTHOR

_Roger Bagula (rlbagulatftn(AT)yahoo.com), _, May 04 2006

Discussion
Fri Mar 30
18:49
OEIS Server: https://oeis.org/edit/global/236
#1 by N. J. A. Sloane at Fri May 19 03:00:00 EDT 2006
NAME

Triangle read by rows: a(n,m) = If(n = 1, then 1, else Prime(n) - 1 + Sum_{k=n..m} (Prime(k + 1) - Prime(k))/2.

DATA

1, 1, 3, 1, 4, 5, 1, 6, 7, 8, 1, 7, 8, 9, 11, 1, 9, 10, 11, 13, 14, 1, 10, 11, 12, 14, 15, 17, 1, 12, 13, 14, 16, 17, 19, 20, 1, 15, 16, 17, 19, 20, 22, 23, 25, 1, 16, 17, 18, 20, 21, 23, 24, 26, 29, 1, 19, 20, 21, 23, 24, 26, 27, 29, 32, 33, 1, 21, 22, 23, 25, 26, 28, 29, 31, 34, 35

OFFSET

1,3

COMMENTS

An improved triangular Goldbach sequence in which the gap sum is taken from a start at n.

EXAMPLE

1

1, 3

1, 4, 5

1, 6, 7, 8

1, 7, 8, 9, 11

1, 9, 10, 11, 13, 14

1, 10, 11, 12, 14, 15, 17

1, 12, 13, 14, 16, 17, 19, 20

1, 15, 16, 17, 19, 20, 22, 23, 25

1, 16, 17, 18, 20, 21, 23, 24, 26, 29

MATHEMATICA

t[n_, m_] := If[n == 1, 1, Prime[n] + Sum[(Prime[k + 1] - Prime[k])/2, {k, n, m}] - 1]; Table[ t[n, m], {m, 11}, {n, m}] // Flatten

CROSSREFS

Main diagonal: A078444, 2nd diagonal: A073273.

Columns 1-8: A000012, A006254, A098090, A089253, A097069, A097338, A097480, A098605.

KEYWORD

nonn,tabl

AUTHOR

Roger Bagula (rlbagulatftn(AT)yahoo.com), May 04 2006

STATUS

approved