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%I M3784 N1541 #37 Nov 06 2023 14:58:26
%S 1,5,9,17,21,29,45,177,18381,22529,24557,26109,34857,41957,67421,
%T 70209,169085,173489,177977,363929,372897
%N Numbers k such that 7*2^k - 1 is prime.
%C k is always of the form 4*j + 1.
%C If k is in the sequence and m=2^(k+2)*3*(7*2^k-1) then phi(m)+sigma(m)=3m (m is in the sequence A011251). The proof is easy. - _Farideh Firoozbakht_, Mar 04 2005
%D H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985, Chap. 4, see pp. 381-384.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Wilfrid Keller, <a href="http://www.prothsearch.com/riesel2.html">List of primes k.2^n - 1 for k < 300</a>
%H H. C. Williams and C. R. Zarnke, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0227095-2">A report on prime numbers of the forms M = (6a+1)*2^(2m-1)-1 and (6a-1)*2^(2m)-1</a>, Math. Comp., 22 (1968), 420-422.
%H <a href="/index/Pri#riesel">Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime</a>
%t Do[ If[ PrimeQ[7*2^n - 1], Print[n]], {n, 1, 2500}]
%o (PARI) v=[ ]; for(n=0,2000, if(isprime(7*2^n-1),v=concat(v,n),)); v
%Y Cf. A050523, A003307, A002235, A046865, A079906, A046866, A005541, A056725, A046867, A079907.
%Y Cf. A032353 (7*2^k+1 is prime).
%K hard,nonn,more
%O 1,2
%A _N. J. A. Sloane_
%E More terms from Douglas Burke (dburke(AT)nevada.edu).
%E More terms from _Hugo Pfoertner_, Jun 23 2004
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