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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202286 Smallest prime which is equal to a multiple of its reversal +/- a prime smaller than itself in exactly n ways. 4
31, 41, 71, 61, 6421, 8501, 8116001, 845534401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence is finite, more specifically there cannot be more than 19 terms. Proof: To have p = k*R(p) -/+ q, with q < p, we must have 0 < k = (p +/- q) / R(p) < 2p / (p/10) = 20, since the prime p cannot end in 0 and therefore R(p) > p/10. (R(p) and p have the same number of digits.) Thus, for a given prime p, there cannot be more than 19 solutions (k=1,...,19) to  p - k*R(p) = +/- q, and therefore no a(n) beyond n=19. - M. F. Hasler, Mar 13 2012, improved following remarks from Hans Havermann, Mar 14 2012

A refined analysis shows that the maximal number is less. On one hand, if R(p) is odd, then only even k can yield a prime. Therefore the maximal number of solutions can only be obtained for p starting with an even digit <= 8, and therefore p/R(p) < 9, thus k < 2p/R(p) < 18, k <= 17. Moreover, R(p) is not a multiple of 3 (since p isn't), therefore 1/3 of the k-values lead to q=0 (mod 3) and are excluded, which leaves at most 11 possibilities. Other k-values lead to q=0 (mod 5), unless p starts with '5'. In any case there cannot be more than 9 solutions. - M. F. Hasler, Mar 14 2012

LINKS

Table of n, a(n) for n=1..8.

Claudio Meller, Números y algo mas...: 833 - Igual a un múltiplo del "inverso" mas/ menos un primo

EXAMPLE

a(4)=61 because 61 = 16 x 2 + 29, 61 = 16 x 3 + 13, 61 = 16 x 4 - 3, and 61 = 16 x 5 - 19.

PROG

(PARI) A202286(n)={ forprime(p=1, default(primelimit), my(r=A004086(p)); 2*p > n*r & sum(k=1, (2*p-1)\r, isprime(abs(p-k*r)))==n & return(p))}  \\ - M. F. Hasler, Mar 14 2012

CROSSREFS

Cf. A099180, A209063, A182239.

Sequence in context: A089442 A243704 A060327 * A141180 A176371 A040987

Adjacent sequences:  A202283 A202284 A202285 * A202287 A202288 A202289

KEYWORD

nonn,base,fini,more

AUTHOR

Claudio Meller, Dec 15 2011, a(3) from Olivier Gérard

EXTENSIONS

a(7)-a(8) from Hans Havermann, Mar 12 2012

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 6 03:02 EST 2016. Contains 278771 sequences.