A122535 -id:A122535 - cp's OEIS frontend

A294147 Initial member of 9 consecutive primes {a, b, c, d, e, f, g, h, i} such that (a + b + c)/3, (d + e + f)/3 and (g + h + i)/3 are all prime.

63487, 462067, 830777, 847507, 1012159, 1049773, 1250611, 1268747, 1372537, 1372559, 1589657, 1988237, 2567557, 2696569, 2874673, 2967317, 3676111, 3718657, 4196987, 4255067, 4550867, 4669333, 5217911, 5225147, 5716031, 6019553, 6103171, 6725657, 6725731, 7143557

Offset: 1

K. D. Bajpai, Oct 23 2017

nonn

			63487 is a term because it is the initial term of 9 consecutive primes {63487, 63493, 63499, 63521, 63527, 63533, 63541, 63559, 63577} = {a, b, c, d, e, f, g, h, i}: the arithmetic mean of three sets, i.e., (a + b + c)/ 3, (d + e + f)/3 and (g + h + i)/3 is prime.

Cf. A000040, A047948, A122535, A293393, A293395.

Select[Partition[Prime@ Range[5*10^5], 9, 1], Function[{a, b, c, d, e, f, g, h, i}, AllTrue[{(a + b + c)/3, (d + e + f)/3, (g + h + i)/3}, PrimeQ]] @@ # &][[All, 1]] (* Michael De Vlieger, Oct 23 2017 *)

A366414 Primes p such that p and the four previous primes are in arithmetic progression.

Original entry on oeis.org

9843139, 37772549, 53868769, 71427877, 78364669, 79080697, 98150141, 99591553, 104437009, 106457629, 111267539, 121174931, 121174961, 168236239, 199450219, 203909011, 207068923, 216618307, 230952979, 234058991, 235524901, 253412437, 263651281, 268843153, 294485483, 296239907

Offset: 1

Harvey P. Dale, Oct 09 2023

			9843019, 9843049, 9843079, 9843109, 9843139 are the 5 consecutive primes starting from A059044(1) and ending at a(1).

Cf. A054643, A122535, A006562, A181424, A054803, A059044, A054800, A122535.

Select[Partition[Prime[Range[10^7]],5,1],Length[Union[Differences[#]]]==1&][[;;,5]]

cp's OEIS Frontend

A294147 Initial member of 9 consecutive primes {a, b, c, d, e, f, g, h, i} such that (a + b + c)/3, (d + e + f)/3 and (g + h + i)/3 are all prime.

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