login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A240233 a(n) is the smallest prime number such that both a(n) + 6n and a(n) + 12n are prime numbers. 1
5, 5, 5, 5, 7, 7, 5, 5, 5, 7, 5, 7, 11, 5, 11, 5, 7, 23, 13, 11, 5, 5, 41, 5, 7, 37, 29, 11, 5, 13, 7, 5, 13, 23, 13, 7, 5, 5, 23, 11, 11, 5, 5, 13, 7, 5, 29, 23, 13, 7, 5, 19, 41, 13, 17, 11, 7, 5, 19, 7, 7, 7, 5, 5, 7, 5, 7, 11, 29, 13, 5, 17, 5, 19, 7, 7, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n), a(n) + 6n, and a(n) + 12n form an arithmetic progression with a common difference of 6n.

If the interval is not a multiple of six, such an arithmetic progression of primes cannot exist unless a(n)=3. For example, 3,5,7 has an interval of 2; 3,7,11 has an interval of 4; and 3,11,19 has an interval of 8, as in A115334 and A206037.

Conjecture: a(n) is defined for all n > 0.

LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000

EXAMPLE

n=1, 6n=6. 5,11,17 are all prime numbers with an interval of 6. So a(1)=5;

...

n=13, 6n=78. 5+78=83, 5+2*78=161=7*23(x); 7+78=85(x); 11+78=89, 11+78*2=167. 11,89,167 are all prime numbers with an interval of 78. So a(13)=11.

MATHEMATICA

Table[diff = n*6; k = 1; While[k++; p = Prime[k]; cp1 = p + diff; cp2 = p + 2*diff; ! ((PrimeQ[cp1]) && (PrimeQ[cp2]))]; p, {n, 77}]

CROSSREFS

Cf. A000040, A115334, A206037, A240087.

Sequence in context: A076568 A139259 A105444 * A033299 A293982 A071577

Adjacent sequences:  A240230 A240231 A240232 * A240234 A240235 A240236

KEYWORD

nonn,easy

AUTHOR

Lei Zhou, Apr 02 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 06:18 EDT 2019. Contains 328292 sequences. (Running on oeis4.)