A051670 Smallest prime that concatenated with all previous terms of sequence forms a prime.

2, 3, 3, 3, 3, 23, 7, 3, 53, 19, 149, 571, 3, 131, 3, 151, 389, 31, 389, 97, 59, 277, 491, 181, 59, 67, 647, 1117, 797, 433, 41, 367, 29, 487, 719, 283, 347, 97, 1103, 193, 821, 13, 29, 31, 947, 619, 167, 229, 479, 271, 1217, 79, 2777, 241, 1361, 751, 83, 4603, 317

Offset: 1

Author

Felice Russo, Dec 15 1999

Keywords

• nonn
• base
• nice

Examples

			The 6th term of the sequence is 23 because that is smallest prime that when concatenated with previous terms 2, 3, 3, 3, 3, produces a prime (2333323).
		

References

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

Links

• Paul Zimmermann, Table of n, a(n) for n = 1..1127 [First 200 terms from T. D. Noe]

Crossrefs

Cf. A048549 and A083758.

Programs

Mathematica

nxt[{lst_,n_}]:=Module[{id=IntegerDigits[lst],np=2},While[ !PrimeQ[ FromDigits[ Join[id, IntegerDigits[np]]]],np=NextPrime[np]];{FromDigits[ Join[id,IntegerDigits[np]]],np}]; Transpose[NestList[nxt,{2,2},60]] [[2]] (* Harvey P. Dale, May 25 2015 *)
nxt[{l_,a_}]:=Module[{k=2},While[CompositeQ[l*10^IntegerLength[k]+ k],k= NextPrime[ k]];{l*10^IntegerLength[k]+k,k}]; NestList[nxt,{2,2},60][[All,2]] (* Harvey P. Dale, Aug 09 2020 *)

Extensions

Extended by T. D. Noe, May 01 2010