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A124939 Prime tetrahedron, read by rows. 0
1, 1, 1, 2, 1, 1, 4, 1, 6, 5, 1, 1, 10, 1, 12, 7, 1, 16, 3, 8, 1, 1, 18, 1, 22, 9, 1, 28, 13, 24, 1, 30, 11, 20, 17, 1, 1, 36, 1, 40, 19, 1, 42, 25, 34, 1, 46, 15, 14, 23, 1, 52, 21, 26, 27, 32, 1, 1, 58, 1, 60, 29, 1, 66, 31, 48, 1, 70, 33, 38, 35, 1, 72, 37, 64, 39, 44, 1, 78, 49, 54, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Each triangular layer of the unique tetrahedron begins with 1, never uses any value other than 1 which has occurred already on this or earlier levels, always uses the least available integer such that the sum of each two consecutive entries is a prime. The number of values of the n-th level is the n-th triangular number A000217(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n. The number of values through the n-th level is the n-th tetrahedral number A000292(n) = C(n+2,3) = n(n+1)(n+2)/6.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 106, 1994.
Kenney, M. J. "Student Math Notes." NCTM News Bulletin. Nov. 1986.
LINKS
Eric Weisstein's World of Mathematics, Prime Triangle.
FORMULA
a(n) flattens the 3-D table so that level 1 (the apex, with only the value 1) occurs first, then level 2 (with values 1, 1, 2), then level 3 ... and for each level, reads that triangle by rows.
EXAMPLE
Tetrahedron begins
=================
1
=================
1
1..2
=================
1
1..4
1..6..5
=================
1
1.10
1.12..7
1.16..3..8
=================
1
1.18
1.22..9
1.28.13.24
1.30.11.20.17
=================
MAPLE
srch := proc(a) local res ; res := 2 ; while true do if isprime(res+op(-1, a)) and not ( res in a ) then RETURN(res) ; fi ; res := res+1 ; od ; end: a := [] ; for lvl from 1 to 10 do for row from 1 to lvl do for col from 1 to row do if col = 1 then anxt := 1 ; else anxt := srch(a) ; fi ; printf("%d, ", anxt) ; a := [op(a), anxt] ; od ; od ; od ; # R. J. Mathar, Jan 13 2007
CROSSREFS
Cf. A000040, A000217, A000292, A036440 Number of ways of arranging row n of the Prime Pyramid, A051239, A051237 Lexicographically earliest Prime Pyramid, read by rows.
Sequence in context: A112987 A125138 A021477 * A187800 A340189 A323873
KEYWORD
easy,nonn,tabf
AUTHOR
Jonathan Vos Post, Nov 13 2006
EXTENSIONS
Corrected and extended by R. J. Mathar, Jan 13 2007
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)