A164312 Numbers n such that k^n + (k-1)^n + ... + 3^n + 2^n + 1 is prime for some k.

1, 2, 4, 8, 16, 1440

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 12 2009

Keywords

• nonn
• hard
• more

Comments

These terms have k-values {2, 2, 2, 2, 2, 5} respectively. When k = 2, the prime mentioned in the definition is given in A164307. - Derek Orr, Jun 06 2014

Examples

			1^1 + 2^1 = 3 is prime (k = 2).
1^2 + 2^2 = 5 is prime (k = 2).
1^4 + 2^4 = 17 is prime (k = 2).
1^8 + 2^8 = 257 is prime (k = 2).
1^16 + 2^16 = 65537 is prime (k = 2).
1^1440 + 2^1440 + 3^1440 + 4^1440 + 5^1440 = 3.287049497374559048967261852*10^1006 = 3287049497374559048967261852 ... 458593539025033893379 is prime (k = 5).
		

Crossrefs

Cf. A000215, A070592, A019434, A092506, A093179, A100270, A123599, A164307.

Programs

Mathematica

lst={};Do[s=0;Do[If[PrimeQ[s+=n^x],AppendTo[lst,x];Print[Date[],x]],{n,4!}],{x,7!}];lst

PARI

a(n)=for(k=1,10^3,if(ispseudoprime(sum(i=1,k,i^n)),return(k)))
n=1;while(n<5000,if(a(n),print1(n,", "));n++) \\ Derek Orr, Jun 06 2014

Extensions

Definition improved by Derek Orr, Jun 06 2014