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A052160 Isolated prime difference equals 6: primes prime(k) such that d(k) = prime(k+1) - prime(k) = 6 but neither d(k+1) nor d(k-1) is 6. 9
23, 31, 61, 73, 83, 131, 233, 271, 331, 353, 383, 433, 443, 503, 541, 571, 677, 751, 991, 1013, 1033, 1063, 1231, 1283, 1291, 1321, 1433, 1453, 1493, 1543, 1553, 1601, 1613, 1621, 1657, 1777, 1861, 1973, 1987, 2011, 2063, 2131, 2207, 2333, 2341, 2351 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Consecutive primes 17, 19, 23, 29, 31 give the pattern of first differences 2, 4, 6, 2 in which the neighboring differences of 6 are not equal to 6.
a(n) - 6 can be prime but not the prime immediately previous to a(n); e.g., 23 - 6 = 17, but the prime 19 lies between the two primes 17 and 23.
LINKS
MAPLE
N:= 3000: # to get all terms <= N
Primes:= select(isprime, [seq(i, i=3..N, 2)]):
d:= Primes[2..-1]-Primes[1..-2]:
R:= select(t -> d[t] = 6 and d[t+1] <> 6 and d[t-1] <> 6, [$2..nops(d)-1]):
Primes[R]; # Robert Israel, May 29 2018
PROG
(PARI) lista(nn) = {vp = primes(nn); vd = vector(#vp-1, k, vp[k+1] - vp[k]); for (i=2, #vd, if ((vd[i] == 6) && (vd[i-1] !=6) && (vd[i+1] != 6), print1(vp[i], ", ")); ); } \\ Michel Marcus, May 29 2018
CROSSREFS
Sequence in context: A330162 A006203 A153635 * A165985 A093014 A165450
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 25 2000
STATUS
approved

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Last modified April 21 10:17 EDT 2024. Contains 371852 sequences. (Running on oeis4.)