A215946 Smallest prime q such that q + prime(n) is power of 6 or 0 if no such q exists.

0, 3, 31, 29, 0, 23, 19, 17, 13, 7, 0, 179, 0, 173, 1249, 163, 157, 0, 149, 0, 1223, 137, 1213, 127, 46559, 0, 113, 109, 107, 103, 89, 0, 79, 78364163957, 67, 0, 59, 53, 1129, 43, 37, 0, 0, 23, 19, 17, 0, 60465953, 1069, 7547, 1063, 7537, 0, 0, 1039, 1033

Offset

1,2

Comments

Such q certainly do not exist if p == 1 (mod 10).

Corresponding exponents of 6 (0 if a(n)=0): 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 3, 0, 3, 4, 3, 3, 0.

Links

Zak Seidov, Table of n, a(n) for n = 1..162

Example

n=2: 3+3=6^1, n=3: 5+31=6^2, n=4: 7+29=6^2, n=6: 13+23=6^2.

Mathematica

s={0, 3}; Do[p=Prime[n]; If[Mod[p, 10]<2, AppendTo[s, 0]; Goto[ne]]; m=Ceiling[Log[6, p]]; While[!PrimeQ[q=6^m-p], m++]; AppendTo[s, q]; Label[ne], {n, 3, 162}]; s

Crossrefs

Cf. A191474.

Sequence in context: A212729 A218357 A090543 * A139090 A238197 A042477

Adjacent sequences: A215943 A215944 A215945 * A215947 A215948 A215949

Keyword

nonn

Author

Zak Seidov, Aug 28 2012

Status

approved