A084671 -id:A084671 - cp's OEIS frontend

A166283 Primes such that the concatenation of its index and itself is a prime.

3, 7, 13, 37, 59, 61, 83, 103, 113, 149, 151, 179, 181, 197, 199, 251, 263, 269, 271, 283, 353, 421, 431, 439, 479, 487, 523, 631, 643, 653, 661, 677, 709, 769, 811, 829, 853, 937, 947, 1019, 1039, 1049, 1051, 1277, 1319, 1399, 1427, 1433, 1489, 1543, 1663

Offset: 1

Robert G. Wilson v, Oct 10 2009

			The prime, 3 has an index of 2, i.e.; pi(3) = 2 and the concatenation, 23 is a prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Complement of 155030, A000040, A084671.

Select[ Prime@ Range@ 273, PrimeQ@ FromDigits@ Join[ IntegerDigits@ PrimePi@#, IntegerDigits@# ] &]
Select[Table[{n,Prime[n]},{n,300}],PrimeQ[#[[1]]*10^IntegerLength[ #[[2]]]+ #[[2]]]&][[All,2]] (* Harvey P. Dale, Jun 01 2017 *)

A262205 Primes that are the concatenation of n, prime(n) and n.

Original entry on oeis.org

353, 7177, 9239, 113111, 5324153, 5726957, 5927759, 6934769, 8141981, 9750997, 101547101, 123677123, 131739131, 153883153, 1791063179, 1891129189, 2011229201, 2071279207, 2311453231, 2491579249, 2631669263, 2691723269, 2791801279

Offset: 1

Altug Alkan, Sep 15 2015

			353 is a prime number that is concatenation of 3, prime(3) and 3.
7177 is a prime number that is concatenation of 7, prime(7) and 7.
9239 is a prime number that is concatenation of 9, prime(9) and 9.

Cf. A084667, A084669, A084670, A084671.

[p: n in [1..400] | IsPrime(p) where p is Seqint(Intseq(n) cat Intseq(NthPrime(n)) cat Intseq(n))]; // Bruno Berselli, Sep 15 2015

f[n_] := Block[{d = IntegerDigits@ n, p = IntegerDigits@ Prime@ n}, FromDigits@ Join[d, p, d]]; Select[f /@ Range@ 300, PrimeQ] (* Michael De Vlieger, Sep 15 2015 *)

for(n=1, 1e3, if(isprime(k=eval(Str(n, prime(n), n))), print1(k", ")))

A243886 Primes p = prime(n): such that p.n and n.p both are prime, where (.) indicates concatenation.

Original entry on oeis.org

661, 1051, 1999, 2179, 3433, 3593, 3719, 4073, 4591, 4733, 5449, 5503, 6079, 6481, 7109, 7211, 7489, 8293, 8513, 9901, 10273, 10529, 11821, 12721, 14107, 14591, 14879, 15263, 15877, 18149, 19559, 22027, 22129, 22571, 23339, 24527, 25357, 26881, 27337, 34259

Offset: 1

K. D. Bajpai, Jun 13 2014

Intersection of A084671 and A166283.

			661 is in the sequence because 661 = prime(121): Concatenations of [661.121 = 661121] and concatenation of [121.661 = 121661] which are also primes.
1051 is in the sequence because 1051 = prime(177): Concatenation of [1051.177 = 1051177] and concatenation of [177.1051 = 1771051] which are also primes.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000040, A084671, A166283.

with(numtheory): with(StringTools): A243886:= proc() local p,k1,k2; p:=ithprime(n); k1:=parse (cat (p,n)); k2:=parse(cat(n,p)); if isprime(k1)and isprime(k2) then RETURN (p); fi; end: seq(A243886 (), n=1..5000);

Select[Prime [Range[5000]], PrimeQ[FromDigits[Join[IntegerDigits [PrimePi [#]], IntegerDigits [#]]]] && PrimeQ [FromDigits [Join [IntegerDigits[#], IntegerDigits [PrimePi [#]]]]] &]

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A166283 Primes such that the concatenation of its index and itself is a prime.

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A262205 Primes that are the concatenation of n, prime(n) and n.

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A243886 Primes p = prime(n): such that p.n and n.p both are prime, where (.) indicates concatenation.

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