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A159260
Numbers k such that 1 + Sum_{i=1..k} 2^prime(i) is prime.
2
1, 2, 4, 5, 8, 43, 127, 251, 1903
OFFSET
1,2
COMMENTS
See A159261 for the primes produced by these n. See A159262 for prime(n), the largest exponent in the sum. The term 1903 produces a probable prime; smaller n produce provable primes. See A122035 for the reducibility of the polynomial obtained by replacing 2 by x.
EXAMPLE
1 is here because 1 + 2^2 = 5 is prime.
2 is here because 1 + 2^2 + 2^3 = 13 is prime.
4 is here because 1 + 2^2 + 2^3 + 2^5 + 2^7 = 173 is prime.
5 is here because 1 + 2^2 + 2^3 + 2^5 + 2^7 + 2^11 = 2111 is prime.
MATHEMATICA
s=1; Reap[Do[s=s+2^Prime[n]; If[PrimeQ[s], Sow[n]], {n, 2000}]][[2, 1]]
CROSSREFS
Sequence in context: A291607 A092752 A152603 * A013103 A012973 A013154
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 07 2009
STATUS
approved