

A024899


Numbers k such that 6*k + 1 is prime.


31



1, 2, 3, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 21, 23, 25, 26, 27, 30, 32, 33, 35, 37, 38, 40, 45, 46, 47, 51, 52, 55, 56, 58, 61, 62, 63, 66, 68, 70, 72, 73, 76, 77, 81, 83, 87, 90, 91, 95, 96, 100, 101, 102, 103, 105, 107, 110, 112, 115, 118, 121, 122, 123, 125, 126, 128, 131, 135, 137
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OFFSET

1,2


COMMENTS

Solutions of the equation (6*n+1)' = 1, where n' is the arithmetic derivative of n.  Paolo P. Lava, Jan 03 2013
For all elements of this sequence there are no (x,y) positive integers such that a(n)=6*x*y+x+y or a(n)=6*x*yxy.  Pedro Caceres, Apr 19 2019


LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)


FORMULA

a(n) = A024892(n)/2 = (A034936(n)+1)/2.  Ray Chandler, Dec 26 2003
a(n) = (A002476(n)1)/6.  Zak Seidov, Aug 31 2016


MAPLE

a := [ ]: for n from 0 to 400 do if isprime(6*n+1) then a := [ op(a), n ]; fi; od: A002476 := n>a[n];


MATHEMATICA

Select[Range@ 140, PrimeQ[6 # + 1] &] (* Michael De Vlieger, Jan 23 2018 *)


PROG

(MAGMA) [n: n in [0..200] IsPrime(6*n+1)] // Vincenzo Librandi, Nov 20 2010
(PARI) select(n>n%6==1, primes(100))\6 \\ Charles R Greathouse IV, Apr 28 2015


CROSSREFS

A002476 gives primes, A091178 gives prime index.
Complement of A046954 relative to A000027.
Sequence in context: A214432 A110086 A107746 * A114518 A066940 A305318
Adjacent sequences: A024896 A024897 A024898 * A024900 A024901 A024902


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling


STATUS

approved



