A070018 a(n) = smallest prime p = prime(k) such that gcd( prime(k+1) - prime(k), prime(k+2) - prime(k+1) ) = 2n.
3, 89, 47, 1823, 1627, 199, 5939, 5591, 15823, 83117, 259033, 16763, 365851, 1074167, 69593, 1625027, 2541289, 255767, 11772613, 3312227, 247099, 23374859, 25767389, 3565931, 21369059, 15340943, 6314393, 59859131, 101996837, 4911251, 70136597, 166185431, 12012677, 198429983, 247837313, 23346737, 298626077
Offset: 1
Keywords
Examples
n=21: a(21)=247099, the consecutive prime triple {247099,247141,247183} determines {42,42} successive differences, the GCD of which is 2n=42.
Programs
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Mathematica
f[x_] := GCD[Prime[x+1]-Prime[x], Prime[x+2]-Prime[x+1]]; t = Table[0, {256} ]; Do[ c = f[n]; If[c <257 && t[[b]] == 0, t[[c]] = n], {n, 2, 1000000} ]; t Prime[t] -
PARI
fp(n, vp) = {for (k=1, #vp-2, if (gcd(vp[k+1] - vp[k], vp[k+2] - vp[k+1]) == 2*n, return (vp[k])););} lista(nn) = {my(vp = primes(10000)); for (n=1, nn, my(p = fp(n, vp)); if (p, print1(p, ", "), break););} \\ Michel Marcus, Aug 29 2019
Formula
a(n) = Min{x : A057467(x)=2n}.
Extensions
Corrected and extended by Michel Marcus, Aug 29 2019