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

1,1

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]

Example

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).

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 *)

Crossrefs

Cf. A048549 and A083758.

Sequence in context: A268607 A069603 A033679 * A089702 A089336 A089335

Adjacent sequences: A051667 A051668 A051669 * A051671 A051672 A051673

Keyword

nonn,base,nice

Author

Felice Russo, Dec 15 1999

Extensions

Extended by T. D. Noe, May 01 2010

Status

approved