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

1,1

Links

Table of n, a(n) for n=1..37.

Formula

a(n) = Min{x : A057467(x)=2n}.

Example

n=21: a(21)=247099, the consecutive prime triple {247099,247141,247183} determines {42,42} successive differences, the GCD of which is 2n=42.

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]

Prog

(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

Crossrefs

Cf. A001223, A057467.

Different from A054682?

Sequence in context: A037112 A093748 A156737 * A054682 A106944 A142252

Adjacent sequences: A070015 A070016 A070017 * A070019 A070020 A070021

Keyword

nonn

Author

Labos Elemer and Benoit Cloitre, Apr 12 2002

Extensions

Corrected and extended by Michel Marcus, Aug 29 2019

Status

approved