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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

Zak Seidov, Table of n, a(n) for n = 1..59542

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

Cf. A088712, A088784.

Sequence in context: A181460 A235687 A321046 * A039354 A043177 A043957

Adjacent sequences:  A269668 A269669 A269670 * A269672 A269673 A269674

KEYWORD

nonn,base

AUTHOR

Zak Seidov, Mar 07 2016

STATUS

approved

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Last modified September 18 00:01 EDT 2021. Contains 347489 sequences. (Running on oeis4.)