This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
for(i=1,9999, isprime(eval(p=Str(prime(i),prime(i+1),prime(i+2)))) & isprime(eval(concat(vecextract(Vec(p),"-1..1"))))& print1(p,", "))
a(1)=711131719 because 711131719 is prime and the concatenation of 7, 11, 13, 17 and 19.
a(5) = 711131719 is the smallest prime which is the concatenation of five consecutive primes 7, 11, 13, 17 and 19.
for(k=1,19, for(i=0,1e9, isprime( eval( p=concat( vector( k,j,Str( prime( i+j )))))) & break); print1(p,", ")) \\ M. F. Hasler, Nov 10 2009
P:= select(isprime,[2,seq(p,p=3..10^4,2)]): select(isprime,[seq(P[i+3]+10^(1+ilog10(P[i+3]))*P[i+2] + 10^(2+ilog10(P[i+3])+ilog10(P[i+2]))*P[i+1] + 10^(3+ilog10(P[i+3])+ilog10(P[i+2])+ilog10(P[i+1]))*P[i], i=1..nops(P)-3)]); # Robert Israel, Apr 14 2016
n=1: 2//3//1 = 231 = 3 * 7 * 11 is not prime, so k<>1. 233 = prime(51), therefore 3 is the first entry. n=2: 3//5//1 = 351 = 3^3 * 13 is not prime, so k <> 1, but 353 = prime(71), therefore 3 is the second entry. n=30: 113//127//1 = 1131271 = prime(87976), so the 30th entry is 1.
read("transforms") ;
A174031 := proc(n) for e from 1 do if isprime(digcatL([ithprime(n),ithprime(n+1),e])) then return e ; end if; end do: end proc:
The prime 113127131137139149 is a concatenation of the consecutive primes 113, 127, 131, 137, 139 and 149.
select(isprime, [seq(parse(cat([seq(ithprime(i), i=n+0..n+5)][])), n=1..500)])[]; # K. D. Bajpai, Mar 24 2014
Select[FromDigits[Flatten[IntegerDigits/@#]]&/@Partition[Prime[Range[ 300]],6,1],PrimeQ] (* Harvey P. Dale, Apr 30 2020 *)
a(2) = 2 because prime(2) = 3, and the concatenation of 2 and 3 gives the prime 23. a(3) = 0 because prime(3) = 5 and there is no prime to concatenate with to give another prime. a(4) = 3 because prime(5) = 7 but the concatenation with 2 gives 27 = 3^3, so it has to be 3 in order to give 37, which is prime.
n=1: 2 // 3 // 3 = 233, which is prime, so a(1) = 3. n=2: 3 // 5 // 2 = 352, which is not prime, but 3 // 5 // 3 = 353 is, so a(2) = 3.
A174034(n)={ n=eval(Str(prime(n),prime(n+1))); for( d=1,99, n*=10; forprime( p=10^(d-1),10^d, isprime(n+p) & return(p)))} \\ M. F. Hasler, Dec 01 2010
concat = lambda xx: Integer(''.join(map(str,xx)))
A174034 = lambda x: next((p for p in Primes() if is_prime(concat([nth_prime(x), nth_prime(x+1), p])))) # D. S. McNeil, Dec 02 2010
172331 is a prime and appears in the sequence because it is the concatenation of prime(7), prime(7+2) and prime(7+4). 233141 is a prime and appears in the sequence because it is the concatenation of prime(9), prime(9+2) and prime(9+4).
with(StringTools): KD := proc() local a,b,d,e; a:=ithprime(n); b:=ithprime(n+2); d:=ithprime(n+4); e:= parse(cat(a,b,d)); if isprime(e) then RETURN (e); fi; end: seq(KD(), n=1..500);
Select[Table[FromDigits[Flatten[{IntegerDigits[Prime[n]], IntegerDigits[Prime[n+2]], IntegerDigits[Prime[n+4]]}]], {n,1,500}],PrimeQ]
235 is in the sequence because concatenation of [2, 3, 5] = 235 = 5 * 47, which is semiprime. 71113 is in the sequence because concatenation of [7, 11, 13] = 71113 = 7 * 10159, which is semiprime. 111317 is not in the sequence because, though 111317 is concatenation of three consecutive primes [11, 13, 17], but it is not semiprime.
with(numtheory): with(StringTools): A244007:= proc() local a,b,c,k,m; a:=ithprime(n); b:=ithprime(n+1); c:=ithprime(n+2);m:=parse(cat(a,b,c)); k:=bigomega(m); if (k)=2 then RETURN (m); fi; end: seq(A244007 (), n=1..100);
A244007 = {}; Do[t = FromDigits[Flatten[IntegerDigits /@ {Prime[n], Prime[n + 1], Prime[n + 2]}]]; If [PrimeOmega[t] == 2, AppendTo[A244007, t]], {n, 100}]; A244007
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