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A290967 Smallest known example of a 3 X 3 X 3 generalized arithmetic progression (GAP) of 27 primes, listed in increasing order. 1
929, 3833, 4079, 6737, 6983, 7229, 8369, 9887, 10133, 11273, 11519, 13037, 14177, 14423, 14669, 15809, 17327, 17573, 18713, 18959, 20477, 21617, 21863, 22109, 24767, 25013, 27917 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

27 primes arranged in a 3 X 3 X 3 cube such that the differences between the numbers in the 3 coordinate directions are constants. The 3 constants are 2904, 3150, and 7440.

The arrangement was found in an undergraduate project at Westfield State College by Jeffrey P. Vanasse and Michael E. Guenette, working under the direction of Mathematics Department faculty members Marcus Jaiclin and Julian F. Fleron.

LINKS

Table of n, a(n) for n=1..27.

Hugo Pfoertner, Illustration of arrangement, copied from announcement of original authors.

Westfield State College, Mathematics Students Make Prime Discovery, ScienceDaily, 18 November 2008.

EXAMPLE

:           -> +2904 ->

:          +-----+-----+-----+

:      |   |  929| 3833| 6737|\

:    +3150 | 4079| 6983| 9887| \

:      V   | 7229|10133|13037|  \

:          +-----+-----+-----+   \

:       \   \   +-----+-----+-----+

:      +7440 \  | 8369|11273|14177|\

:         \   \ |11519|14423|17327| \   \

:              \|14669|17573|20477|  \ +7440

:               +-----+-----+-----+   \   \

:                \   +-----+-----+-----+

:                 \  |15809|18713|21617|   |

:                  \ |18959|21863|24767| +3150

:                   \|22109|25013|27917|   V

:                    +-----+-----+-----+

:                     -> +2904 ->

MAPLE

sort([seq(seq(seq(929+i*3150+k*2904+j*7440, k=0..2), i=0..2), j=0..2)])[];

# Alois P. Heinz, Aug 16 2017

CROSSREFS

Cf. A005115.

Sequence in context: A219526 A249535 A289727 * A109184 A219066 A068651

Adjacent sequences:  A290964 A290965 A290966 * A290968 A290969 A290970

KEYWORD

nonn,fini,full

AUTHOR

Hugo Pfoertner, Aug 15 2017

STATUS

approved

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)