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 A091421 Numbers n such that n#*2^n - 1 is prime, where n# is product of prime numbers (primorials). 1
 1, 2, 3, 4, 6, 7, 8, 15, 19, 31, 68, 69, 78, 82, 162, 210, 524, 770, 1058, 1437, 1730, 3977 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 1# = 2 2# = 2*3 = 6 3# = 2*3*5 = 30. No more terms < 5000. - L. Joris Perrenet, Mar 17 2020 LINKS Table of n, a(n) for n=1..22. EXAMPLE a(1)=1 because 1#*2^1 - 1 = 3 is prime. a(2)=2 because 2#*2^2 - 1 = 23 is prime. MATHEMATICA For[n = 1, n < 60, n++, If[PrimeQ[2^n*Product[Prime[i], {i, 1, n}] - 1], Print[n]]] (* Stefan Steinerberger, Feb 06 2006 *) PROG (PARI) pp(n)= s=1; for(i=1, n, s=s*prime(i)); return(s); f(n)=pp(n)!*2^n -1; for (i=1, 500, if(isprime(f(i)), print1(i, ", "))) CROSSREFS Cf. A002110. Sequence in context: A096360 A039087 A093710 * A138936 A135604 A345437 Adjacent sequences: A091418 A091419 A091420 * A091422 A091423 A091424 KEYWORD nonn,hard,more AUTHOR Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 02 2004 EXTENSIONS a(17) from Stefan Steinerberger, Feb 06 2006 a(18)-a(22) from L. Joris Perrenet, Mar 17 2020 STATUS approved

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Last modified December 7 11:26 EST 2023. Contains 367650 sequences. (Running on oeis4.)