A012883 Numbers in which every prefix (in base 10) is 1 or a prime.

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 53, 59, 71, 73, 79, 113, 131, 137, 139, 173, 179, 191, 193, 197, 199, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 1319, 1373, 1399, 1733, 1913, 1931, 1933, 1973, 1979, 1993, 1997, 1999

Offset: 1

Author

Larry Calmer (larry(AT)wri.com), Simon Plouffe

Keywords

• nonn
• fini
• full
• nice
• base

Links

• T. D. Noe, Table of n, a(n) for n=1..147 (complete sequence)

Crossrefs

Cf. A024770 (every prefix is prime).

Programs

Mathematica

max = 10^10; truncate[p_] := If[q = Quotient[p, 10]; q == 1 || PrimeQ[q], q, p]; ok[p_] := FixedPoint[truncate, p] < 10; p = 1; cnt = 2; A012883 = Join[{1}, Reap[While[(p = NextPrime[p]) < max, If[ok[p], Print[cnt++, " ", p]; Sow[p]]]][[2, 1]]] (* Jean-François Alcover, Nov 23 2015 *)

PARI

for(n=1, 1e4, k=n; while(isprime(n) || n==1, c=n; n=(c-lift(Mod(c, 10)))/10); if(n==0, print1(k, ", ")); n=k) \\ Altug Alkan, Nov 23 2015

Extensions

Last term is A094335(10) = 1979339339 (confirmed by David W. Wilson ).