A083758 Lexicographically earliest infinite sequence of distinct primes such that the concatenation of the initial n terms is a prime for all n >= 1.

2, 3, 11, 7, 41, 31, 17, 163, 23, 79, 197, 241, 29, 37, 59, 193, 227, 229, 239, 439, 929, 337, 257, 1447, 509, 19, 293, 1723, 1619, 937, 179, 367, 251, 1063, 4241, 1291, 521, 1951, 443, 139, 191, 1753, 1217, 673, 53, 883, 809, 109, 5381, 3733, 311, 967, 449

Offset

1,1

Comments

Conjecture: every prime except 5 is a term.

However, after 1000 terms, 13, 47, 61, ... are still missing. A158521 suggests there is no intrinsic reason why 13 should not eventually appear. - N. J. A. Sloane, Oct 21 2020

Links

Paul Zimmermann, Table of n, a(n) for n = 1..1479 [First 800 terms from Giorgos Kalogeropoulos; first 1156 terms from Metin Sariyar]

Example

2 is a prime.
2||3 = 23 is a prime.
2||3||7 = 3*79 but 2||3||11 = 2311 is a prime
So is 23117.  And so on.

Mathematica

a[1]=2; a[n_]:=a[n]=Module[{v=1, k=Table[a[m], {m, n-1}]}, While[PrimeQ[FromDigits@Join[Flatten[IntegerDigits/@k], IntegerDigits[t=Prime[v]]]]==False||MemberQ[k, t], v++]; k=Join[k, {t}]; t]; Table[a[i], {i, 60}]  (* Giorgos Kalogeropoulos, May 28 2019 *)

Prog

(PARI) a083758(m)={my(np=1000*m, pused=vectorsmall(np), digp=[]); for(n=1, m, my(found=0); for(k=1, np, if(!pused[k], my(add=digits(prime(k)), pc=concat(digp, add)); if(ispseudoprime(fromdigits(pc)), print1(prime(k), ", "); digp=pc; pused[k]=1; found=1; break))); if(!found, break))};
a083758(53) \\ Hugo Pfoertner, Oct 21 2020

Crossrefs

Cf. A051670, A083759, A338072, A338073, A051670.

See also A158521.

Sequence in context: A145077 A127376 A086146 * A127494 A320264 A335173

Adjacent sequences: A083755 A083756 A083757 * A083759 A083760 A083761

Keyword

base,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003

Extensions

More terms from Sean A. Irvine, Dec 15 2009

Edited by N. J. A. Sloane, Oct 19 2020 following a comment from David James Sycamore

Status

approved