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A036261 Triangle of numbers arising from Gilbreath's conjecture: successive absolute differences of primes (read by antidiagonals upwards, omitting the initial row of primes). 7
1, 1, 2, 1, 0, 2, 1, 2, 2, 4, 1, 2, 0, 2, 2, 1, 2, 0, 0, 2, 4, 1, 2, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0, 2, 4, 1, 2, 0, 0, 0, 0, 0, 2, 6, 1, 0, 2, 2, 2, 2, 2, 2, 4, 2, 1, 0, 0, 2, 0, 2, 0, 2, 0, 4, 6, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 4, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

R. K. Guy, Unsolved Problems Number Theory, A10.

C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 410.

LINKS

T. D. Noe, Rows n=1..100 of triangle, flattened

A. M. Odlyzko, Iterated absolute values of differences of consecutive primes, Math. Comp. 61 (1993), 373-380.

EXAMPLE

Table begins (conjecture is leading term is always 1):

  2 3 5 7 11 13 17 19 23 ...

  1 2 2 4  2  4  2  4 ...

  1 0 2 2  2  2  2 ...

  1 2 0 0  0, 0 ...

  1 2 0 0  0 ...

  1 2 0 0 ...

  ...

MATHEMATICA

max = 15; triangle = Rest[ NestList[ Abs[ Differences[#] ]& , Prime[ Range[max] ], max] ]; Flatten[ Table[ triangle[[n-k+1, k]], {n, 1, max-1}, {k, 1, n}]] (* Jean-Fran├žois Alcover, Jan 23 2012 *)

CROSSREFS

See A036262, which is the main entry for this array.

Sequence in context: A035443 A180430 A246369 * A140575 A091917 A025657

Adjacent sequences:  A036258 A036259 A036260 * A036262 A036263 A036264

KEYWORD

tabl,easy,nice,nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Naohiro Nomoto, May 22 2001

STATUS

approved

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Last modified November 18 19:06 EST 2017. Contains 294894 sequences.