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`%I #13 Dec 28 2021 04:20:27
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`%S 0,1,2,3,6,8,583,6393,9715,33288,50011,126113,31172165
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`%N Record values in A057192, until A350118(n) reaches the smallest prime Sierpiński number and then sequence terminates with a(n) = -1.
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`%F a(n) = A057192(primepi(A350118(n))).
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`%e Let b(p) be the smallest m such that p*2^m + 1 is prime. We have a(1) = b(2) = 0.
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`%e The least prime p such that b(p) > 0 is p = 3 with b(3) = 1, so a(2) = 1.
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`%e The least prime p such that b(p) > 1 is p = 7 with b(7) = 2, so a(3) = 2.
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`%e The least prime p such that b(p) > 2 is p = 17 with b(17) = 3, so a(4) = 3.
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`%e The least prime p such that b(p) > 3 is p = 19 with b(19) = 6, so a(5) = 6.
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`%e The least prime p such that b(p) > 6 is p = 31 with b(31) = 8, so a(6) = 8.
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`%e The least prime p such that b(p) > 8 is p = 47 with b(47) = 583, so a(7) = 583.
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`%o (PARI) b(p) = for(k=0, oo, if(isprime(p*2^k+1), return(k)))
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`%o list(lim) = if(lim>=2, my(v=[0],r=0); forprime(p=2, lim, if(b(p)>r, r=b(p); v=concat(v,r))); v) \\ gives a(n) for A350118(n) <= lim
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`%Y Cf. A057192, A350118, A103964, A076336 (Sierpiński numbers).
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`%K sign,fini,hard,more
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`%O 1,3
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`%A _Jianing Song_, Dec 14 2021
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