The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A269671 Integers n such that the concatenation of prime(n) and prime(n+1) and also concatenation of prime(n+1) and prime(n) are prime. 1
46, 51, 55, 71, 99, 119, 164, 298, 345, 461, 509, 523, 588, 668, 779, 827, 844, 848, 999, 1100, 1151, 1215, 1306, 1321, 1408, 1553, 1568, 1616, 1779, 1900, 1931, 1953, 2102, 2150, 2221, 2444, 2653, 2677, 3116, 3405, 3527, 3731, 3776, 3890, 3898, 3989, 4070, 4188, 4257, 4546, 4556, 4574, 4681, 4694, 4846, 4947, 4948, 4974 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Difference between prime(n) and prime(n+1) is a multiple of 6, otherwise concatenation prime(n)//prime(n+1) is divisible by 3.
LINKS
EXAMPLE
prime(46)=199, prime(47)=211 and both 199211 and 211199 are prime,
prime(51)=233, prime(51)=239 and both 233239 and 239233 are prime,
prime(9999972)=179424263, prime(9999973)=179424269 and both 179424263179424269 and 179424269179424263 are prime.
MATHEMATICA
PrimePi/@Select[Partition[Prime[Range[5000]], 2, 1], AllTrue[{FromDigits[ Join[ IntegerDigits[ #[[1]]], IntegerDigits[#[[2]]]]], FromDigits[ Join[ IntegerDigits[#[[2]]], IntegerDigits[#[[1]]]]]}, PrimeQ]&][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 14 2021 *)
PROG
(PARI) isok(n) = {my(sp = Str(prime(n))); my(sq = Str(prime(n+1))); isprime(eval(concat(sp, sq))) && isprime(eval(concat(sq, sp))); } \\ Michel Marcus, Mar 07 2016
CROSSREFS
Sequence in context: A235687 A365009 A321046 * A039354 A043177 A043957
KEYWORD
nonn,base
AUTHOR
Zak Seidov, Mar 07 2016
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 05:37 EDT 2024. Contains 372807 sequences. (Running on oeis4.)