

A196779


a(n) is the smallest number m such that no prime takes the form of n^m+/n^k+/1, while 0 <= k < m and m > 1.


0



1147, 113, 113, 400, 866, 131, 399, 32, 26, 29, 23, 58, 77, 21, 42, 3, 817, 4, 2, 37, 80, 29, 181, 39, 120, 382, 76, 5, 29, 20, 48, 19, 36, 7, 43, 7, 62, 22, 7, 43, 5, 17, 23, 44, 52, 137, 103, 2, 5, 49, 31, 10, 30, 5, 25, 25, 49, 10, 72, 50, 13, 4, 7, 6
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OFFSET

5,1


COMMENTS

Conjecture: a(n) has finite value when a>4
already tested: a(4)>2364; a(3)>7399; and a(2)>9594.
Hypothesis is that a(2), a(3), and a(4) are infinite.
Mathematica program ran about an hour and gave the first 96 items.
When n is larger, a(n) tends to be 2 for most of n.


LINKS

Table of n, a(n) for n=5..68.


EXAMPLE

n=5, there is no prime number in the form of 5^1147+/5^k+/1 for 0 <= k < 1147


MATHEMATICA

Table[i = 1; While[i++; c1 = b^i; cs = {};
Do[c2 = b^j; cp = c1 + c2 + 1;
If[PrimeQ[cp], cs = Union[cs, {cp}]];
cp = c1 + c2  1; If[PrimeQ[cp], cs = Union[cs, {cp}]];
cp = c1  c2 + 1; If[PrimeQ[cp], cs = Union[cs, {cp}]];
cp = c1  c2  1;
If[PrimeQ[cp], cs = Union[cs, {cp}]], {j, 0, i  1}];
ct = Length[cs]; ct > 0]; i, {b, 5, 100}]


CROSSREFS

Cf. A196697, A196698, A196778.
Sequence in context: A260977 A227478 A190924 * A180344 A031785 A274297
Adjacent sequences: A196776 A196777 A196778 * A196780 A196781 A196782


KEYWORD

nonn


AUTHOR

Lei Zhou, Oct 06 2011


STATUS

approved



