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 A276511 Primes that are equal to the sum of the prime factors of some perfect number. 3
 5, 11, 139, 170141183460469231731687303715884105979 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes of the form 2^n + 2*n - 3 such that 2^n - 1 is also prime. Conjectures (defining x = 170141183460469231731687303715884105727 = A007013(4)): (1) 2^x + 2*x - 3 is in this sequence; (2) a(5) = 2^x + 2*x - 3 (see comments of A276493); (3) primes of A007013 are Mersenne prime exponents A000043, i.e., x is new exponent in A000043. LINKS EXAMPLE a(1) = 5 because 2^2-1 = 3 and 2^2+2*2-3 = 5 are primes, a(2) = 11 because 2^3-1 = 7 and 2^3+2*3-3 = 11 are primes, a(3) = 139 because 2^7-1 = 127 and 2^7+2*7-3 = 139 are primes. MAPLE A276511:=n->`if`(isprime(2^n-1) and isprime(2^n+2*n-3), 2^n+2*n-3, NULL): seq(A276511(n), n=1..10^3); # Wesley Ivan Hurt, Sep 07 2016 PROG (MAGMA) [2^n+2*n-3: n in [1..200] | IsPrime(2^n-1) and IsPrime(2^n+2*n-3)]; CROSSREFS Subsequence of A192436. Cf. A000043, A000396, A000668, A007013, A100118, A276493. Sequence in context: A083418 A266527 A267078 * A020453 A036932 A162252 Adjacent sequences:  A276508 A276509 A276510 * A276512 A276513 A276514 KEYWORD nonn,more AUTHOR Juri-Stepan Gerasimov, Sep 06 2016 EXTENSIONS Name suggested by Michel Marcus, Sep 07 2016 STATUS approved

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Last modified April 14 00:42 EDT 2021. Contains 342941 sequences. (Running on oeis4.)