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A184248
Primes, q, such that for three consecutive primes, p, q & r, with p<q<r, (r - q)/(q - p) is an integer.
3
3, 5, 7, 13, 19, 31, 43, 53, 61, 73, 103, 109, 139, 151, 157, 173, 181, 193, 199, 211, 229, 241, 257, 263, 271, 283, 313, 349, 373, 401, 421, 433, 463, 467, 491, 509, 523, 563, 571, 593, 601, 607, 619, 643, 653, 661, 733, 743, 761, 811, 823, 829, 859
OFFSET
1,1
COMMENTS
The distance between the cited prime above to its immediate successor is divisible by the distance from that prime to its immediate predecessor.
Intersection(A184247, A184248): 5, 53, 157, 173, 211, .., = A006562: Balanced primes (of order 1).
LINKS
MATHEMATICA
fQ[n_] := Block[{p = NextPrime[n, -1], q = n, r = NextPrime[n]}, IntegerQ[(r - q)/(q - p)]]; Select[ Prime@ Range@ 150, fQ]
Transpose[Select[Partition[Prime[Range[200]], 3, 1], IntegerQ[(#[[3]]- #[[2]])/ (#[[2]]-#[[1]])]&]][[2]] (* Harvey P. Dale, Mar 30 2014 *)
CROSSREFS
Cf. A184247.
Sequence in context: A100859 A336369 A111703 * A206023 A067829 A084696
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Jan 10 2011
STATUS
approved