A077258 -id:A077258 - cp's OEIS frontend

A076707 Ordered differences without repetitions between two successive prime powers of prime numbers.

1, 2, 3, 4, 5, 10, 12, 16, 17, 18, 30, 38, 41, 46, 54, 72, 74, 94, 120, 128, 138, 139, 168, 186, 199, 240, 248, 250, 260, 271, 286, 288, 312, 316, 354, 356, 370, 408, 424, 432, 496, 546, 552, 582, 600, 602, 618, 678, 720, 768, 792, 836, 840, 876, 890, 894, 912

Offset: 1

Zak Seidov, Oct 26 2002

nonn

Several entries are represented by at least two differences: 4 (which equals 8-4 & 125-121), 168, 312, 600, 768, 792, 912, 1848, 2472, etc.

			250 = 161051 - 160801 = 11^5 - 401^2.

Cf. A053810, A075308, A077257, A077258.

pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^16]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^16]]]}]]]; l = Length[pp]; b = Take[pp, -l + 1] - Take[pp, l - 1]; Take[ Union[a], 57]

Edited and corrected by Robert G. Wilson v, Oct 31 2002

A077257 Differences between two successive prime powers of prime numbers (A076707) in more than one way.

Original entry on oeis.org

4, 168, 312, 600, 768, 792, 912, 1848, 2472, 3048, 3192, 3288, 3528, 3720, 4008, 4920, 5160, 5208, 5928, 6072, 6792, 6840, 6888, 7080, 7512, 7728, 7800, 8520, 8760, 10632, 11400, 11880, 11928, 12792, 13200, 13440, 13560, 14280, 14640, 15960

Offset: 1

Zak Seidov and Robert G. Wilson v, Oct 31 2002

nonn

			4 = 8-4 = 125-121, 168 = 529-361 = 1849-1681, 312 = 841-529 = 1681-1369.
It is interesting that 529 is a member of the last two examples.
6888 is the first one to be represented in just three ways.
4920 is the first one to be represented in four ways.

Cf. A053810, A075308, A076707, A077258.

pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^16]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^16]]]}]]]; l = Length[pp]; b = Sort[ Take[pp, -l + 1] - Take[pp, l - 1]]; Union[ b[[ Select[ Range[355], b[[ # ]] == b[[ # + 1]] &]]]]

cp's OEIS Frontend

A076707 Ordered differences without repetitions between two successive prime powers of prime numbers.

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