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.

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

Offset: 1

Author

Labos Elemer, Jan 25 2000

Keywords

• nonn

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

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001223, A033451, A047948.

Programs

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

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