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 A274025 Primes n such that Sum_{k = primes
 5, 691, 2399, 3433, 5099, 6217, 7451, 9007, 10253, 10883, 16561, 21839, 23189, 25679, 26501, 30661, 39097, 41443, 43591, 48119, 50893, 56009, 60293, 64927, 65537, 78979, 79829, 85853, 98669, 100403, 105491, 115981, 124783, 140557, 142547, 148013, 149953, 164113, 166219, 169249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS As 0 < k < n, k mod n == k, so Sum_{k = primes 3. - David A. Corneth, Jun 07 2016 LINKS Robert Israel, Table of n, a(n) for n = 1..1003 EXAMPLE 2 mod 5 = 2, 3 mod 5 = 3 and 2 + 3 = 5 is prime; 5 mod 2 = 1, 5 mod 3 = 2 and 1 + 2 = 3 is prime. MAPLE with(numtheory): P:=proc(q) local a, b, j, k, n; for j from 1 to q do n:=ithprime(j); a:=0; b:=0; for k from 1 to n-1 do if isprime(k) then a:=a+k; b:=b+(n mod k); fi; od; if isprime(a) and isprime(b) then print(n); fi; od; end: P(10^6); # Alternative: N:= 10^6: # to get all entries <= N Primes:= select(isprime, [2, seq(i, i=3..N, 2)]): PS:= ListTools:-PartialSums(Primes): count:= 0: for i from 2 to nops(Primes) do    n := Primes[i];    if isprime(PS[i-1]) and isprime(add(n mod Primes[j], j=1..i-1)) then      count:= count+1;      A[count]:= n;    fi od: seq(A[i], i=1..count); # Robert Israel, Jun 07 2016 PROG (PARI) is(n) = {if(isprime(n), my(nk, kn, u=prime(primepi(n-1))); forprime(k=2, u, kn+=k; nk+=n%k); isprime(kn)&&isprime(nk), 0)} \\ David A. Corneth, Jun 07 2016 CROSSREFS Cf. A000040, A000720, A007504, A151799. Sequence in context: A000367 A176546 A092133 * A281585 A071772 A201005 Adjacent sequences:  A274022 A274023 A274024 * A274026 A274027 A274028 KEYWORD nonn,easy AUTHOR Paolo P. Lava, Jun 07 2016 STATUS approved

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Last modified October 16 20:34 EDT 2018. Contains 316275 sequences. (Running on oeis4.)