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 A222558 Least prime p such that 2*n*p is a sum of 10^6 subsequent primes. 0

%I #11 Feb 25 2013 19:39:55

%S 3736971300983,1868582442157,1245659681423,934275734321,747425233469,

%T 622762733249,534156162737,467093343419,415824854441,373728877943,

%U 339743670103,311538175027,287741107327,266994001331,249114901193,233613943273,219815919913,208214150917

%N Least prime p such that 2*n*p is a sum of 10^6 subsequent primes.

%C Indices of first primes are: 64, 89, 65, 81, 84, 13, 338, 35, 768, 105, 91, 256, 537, 186, 32, 174, 51, 1469, 519, 277, 2132, 232, 241, 310, 179, 744, 1835, 535, 787, 167, 664, 1538, 1253, 484, 620, 1450, 961, 649, 1472, 166, 480, 918, 107, 418, 173, 370, 871, 1967, 71, 534.

%C First primes are: 311, 461, 313, 419, 433, 41, 2273, 149, 5849, 571, 467, 1619, 3877, 1109, 131, 1033, 233, 12281, 3719, 1787, 18671, 1459, 1523, 2053, 1063, 5653, 15737, 3853, 6037, 991, 4967, 12917, 10211, 3461, 4583, 12109, 7573, 4817, 12323, 983, 3413, 7187, 587, 2887, 1031, 2531, 6763, 17047, 353, 3851.

%e a(1) = 3736971300983 = (p(64)+...+p(1000063)/2 = (311 +... 15486871)/2

%e a(2) = 1868582442157 = (p(289)+...+p(1000288)/2 = (461 +... 15487253)/4

%t Do[s = 7472966967499 ; a = 2; b = 15485863; Do[s = s - a + (b = NextPrime[b]); a = NextPrime[a]; If[PrimeQ[s/m] , Print[{m, k, a, b, s/m}]; Break[]], {k, 2, 10^6}], {m, 2, 100, 2}]

%Y Cf. A099824, A123086.

%K nonn

%O 1,1

%A _Zak Seidov_, Feb 25 2013

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Last modified May 26 16:43 EDT 2024. Contains 372840 sequences. (Running on oeis4.)