A094489 Primes p such that 2^j+p^j are primes for j=0,1,4,32.

59, 5417, 19079, 33827, 136949, 181871, 242519, 284897, 421607, 452537, 552401, 598187, 962681, 1068251, 1081979, 1163231, 1317761, 1760279, 1801361, 1891499, 1895081, 1919459, 2056907, 2131601, 2427461, 2557601, 2579177, 2826737

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..400

Example

For j=0 1+1=2 is prime; also terms should be lesser-twin-primes
because of p^1+2^1=p+2=prime; 3rd and 4th conditions are as
follows: prime=p^4+16 and prime=2^32+p^32.

Mathematica

{ta=Table[0, {100}], u=1}; Do[s0=2; s1=Prime[j]+2; s2=4+Prime[j]^2; s8=2^32+Prime[j]^32; If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s8], Print[{j, Prime[j]}]; ta[[u]]=Prime[j]; u=u+1], {j, 1, 1000000}]
Select[Prime[Range[210000]], AllTrue[{2+#, 16+#^4, 2^32+#^32}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 13 2015 *)

Crossrefs

Cf. A082101, A094473-A094488.

Sequence in context: A278367 A198509 A258269 * A235215 A178066 A191947

Adjacent sequences: A094486 A094487 A094488 * A094490 A094491 A094492

Keyword

nonn

Author

Labos Elemer, Jun 01 2004

Status

approved