

A240087


Smallest difference to start a prime arithmetic progression of three or more terms with the nth prime number.


3



2, 6, 6, 18, 24, 36, 24, 24, 30, 6, 36, 6, 18, 12, 18, 24, 6, 42, 78, 78, 24, 48, 12, 6, 6, 48, 30, 84, 18, 12, 66, 60, 84, 24, 6, 36, 18, 6, 54, 84, 48, 36, 18, 36, 12, 126, 54, 6, 42, 18, 54, 36, 6, 12, 48, 24, 6, 30, 36, 24, 108, 90, 36, 18, 42, 66, 36, 6
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OFFSET

2,1


COMMENTS

It is conjectured that this sequence is defined for all odd prime numbers.


LINKS

Lei Zhou, Table of n, a(n) for n = 2..10001
Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.


FORMULA

prime(n) + a(n)*k, with n >= 2, for k = 0, 1, 2, ..., kmax(n), with kmax(n) >= 2, are primes, but prime(n)  a(n) is not a prime. prime(n)= A000040(n).  Wolfdieter Lang, Apr 17 2014


EXAMPLE

n=2: the second prime number is 3; 3, 5, 7 form a 3term prime arithmetic progression with difference 2. So a(2) = 2.
n=3: the third prime is 5; 5, 11, 17, 23, 29 form a 5term prime arithmetic progression with difference 6, and this is the smallest difference to obtain three or more terms, hence a(3) = 6.
n=5: the fifth prime number is 11. Although 11, 17, 23, 29 form a 4term prime arithmetic progression with difference 6, this prime arithmetic progression actually starts with 5 (see n=3). 11, 29, 47 form a 3term prime arithmetic progression with difference 18. So a(5) = 18.


MATHEMATICA

Table[p = Prime[n]; pt = p; While[pt = NextPrime[pt]; diff = pt  p; ! ((PrimeQ[pt + diff]) && ((! (PrimeQ[p  diff]))  (p < diff)))]; diff, {n, 2, 69}]


CROSSREFS

Cf. A000040.
Sequence in context: A019076 A197109 A111410 * A083774 A081518 A258702
Adjacent sequences: A240084 A240085 A240086 * A240088 A240089 A240090


KEYWORD

nonn


AUTHOR

Lei Zhou, Mar 31 2014


EXTENSIONS

Name and examples edited, link added.  Wolfdieter Lang, Apr 17 2014


STATUS

approved



