A051670 -id:A051670 - cp's OEIS frontend

A051671 Smallest positive number whose digits concatenated with all previous terms forms a perfect square.

4, 9, 284, 61209, 14204828164, 4440027571600000000001, 7667716927194638935286982918857620344809476

Offset: 0

			284 belongs to the sequence because 49284=222^2.

A. Murthy, Smar. Notions J. Vol. 11 N. 1-2-3 Spring 2000.

Cf. A048559, A048560, A051670.

More terms from Patrick De Geest, Dec 15 1999

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

Original entry on oeis.org

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

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

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

			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.

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

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

See also A158521.

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 *)

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

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

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A051671 Smallest positive number whose digits concatenated with all previous terms forms a perfect square.

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

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