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.

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

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: A235687 A365009 A321046 * A039354 A043177 A043957

Adjacent sequences: A269668 A269669 A269670 * A269672 A269673 A269674

Keyword

nonn,base

Author

Zak Seidov, Mar 07 2016

Status

approved