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A295741
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a(n) is smallest divisor d of the n-th primorial such that d + prime(n)#/d is prime.
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1
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1, 1, 1, 1, 1, 1, 2, 5, 6, 10, 2, 1, 2, 11, 7, 2, 41, 2, 5, 5, 5, 3, 51, 10, 3, 14, 37, 10, 7, 2, 17, 17, 62, 21, 3, 38, 17, 47, 13, 17, 13, 7, 21, 83, 10, 138, 10, 26, 2, 7, 19, 31, 15, 13, 5, 23, 103, 19, 5, 95, 61, 6, 15, 2, 35, 13, 19, 65, 39, 7, 43, 73, 13, 26, 97, 1, 91, 2, 78, 19, 39, 34, 167, 82, 10, 38, 66, 58, 2, 46, 71
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OFFSET
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0,7
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COMMENTS
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Conjecture: a(n) < prime(n)^2 for n > 0.
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LINKS
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EXAMPLE
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a(3) = 1 because 1 + prime(3)#/1 = 1 + 2*3*5 = 31 and 31 is a prime;
a(6) = 2 because 2 + prime(6)#/2 = 2 + 2*3*5*7*11*13/2 = 15017 and that is a prime;
a(7) = 5 because 5 + prime(7)#/5 = 5 + 2*3*5*7*11*13*17/5 = 102107 which is a prime; etc.
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MATHEMATICA
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f[n_] := Block[{d = 1, p = Fold[Times, 1, Prime@ Range@ n]}, While[ !PrimeQ[d + p/d], d++]; d]; Array[f, 90]
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PROG
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(PARI) a(n)=my(P=vecprod(primes(n))); for(d=1, P, if(P%d==0 && ispseudoprime(d+P/d), return(d))) \\ Charles R Greathouse IV, Nov 27 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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