A074953 -id:A074953 - cp's OEIS frontend

A260517 Numbers equidistant from twin prime pairs that are also equidistant from numbers equidistant from twin prime pairs.

51, 105, 144, 165, 234, 255, 276, 630, 1041, 2289, 2325, 2466, 4251, 5460, 9006, 9699, 10380, 10479, 12006, 13701, 14166, 15690, 18090, 19425, 20190, 20295, 21540, 26706, 26796, 32487, 32871, 33684, 33789, 35520, 37455, 38661, 41685, 42771, 46515, 47760

Offset: 1

Peter Woodward, Jul 27 2015

nonn

			165 is a term because it is equidistant from 144 and 186. 144 and 186 are both equidistant from twin primes, according to A074953.

Robert G. Wilson v, Table of n, a(n) for n = 1..1257

Cf. A001097 (Twin primes), A074953 (Numbers equidistant from twin prime pairs).

t = Select[ Prime@ Range@ 5000, PrimeQ[# + 2] &]; d = Differences@ t; (t[[#+1]] + t[[#+2]]& /@ Select[ Range[ Length[d] - 2], d[[#]] == d[[#+2]] &])/2 + 1 (* Robert G. Wilson v, Jul 29 2015 *)

A074931 Primes p such that 3p is equidistant from consecutive prime twin pairs.

Original entry on oeis.org

3, 5, 17, 29, 41, 71, 149, 281, 317, 347, 359, 397, 647, 751, 787, 857, 907, 1093, 1279, 1381, 1511, 1531, 1663, 1783, 2447, 2683, 2803, 3271, 3323, 4019, 4153, 4513, 4567, 4639, 5557, 5647, 5801, 5923, 6599, 6659, 6911, 7013, 7573, 7883, 9187, 9257, 9431

Offset: 1

N. Fernandez (primeness(AT)borve.org), Zak Seidov, Oct 10 2002

nonn

Numbers equidistant from consecutive twins (see A074953) are multiples of 3 and they may be almost primes only of form 3*prime. In the sequence, these primes are given. Also: A001748 (3*prime 2-almost-primes) and A001358 (all 2-almost-primes).

			17 is in the sequence because 3 * 17 = 51 is equidistant between {41, 43} and {59, 61}.
19 is not in the sequence because 3 * 19 = 57, which is much closer to {59, 61} than to {41, 43}.

Cf. A001358, A001748, A074953.

New name from Charles R Greathouse IV, Oct 12 2013

cp's OEIS Frontend

A260517 Numbers equidistant from twin prime pairs that are also equidistant from numbers equidistant from twin prime pairs.

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