A107812 a(1) = prime(12), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

37, 3, 13, 11, 17, 7, 47, 41, 19, 29, 2, 23, 31, 43, 53, 5, 59, 79, 67, 61, 71, 73, 83, 89, 97, 107, 101, 103, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset

1,1

Comments

a(n) = prime(n) for almost all n. Probably a(n) = prime(n) for all n > N for some N, but N must be very large. - Charles R Greathouse IV, Jul 20 2011

Links

Table of n, a(n) for n=1..59.

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jul 20 2011

Mathematica

p=Prime[12]; b={p}; d=p; Do[Do[r=Prime[c]; If[FreeQ[b, r]&&Intersection@@IntegerDigits/@{d, r}=!={}, b=Append[b, r]; d=r; Break[]], {c, 1000}], {k, 60}]; b

Prog

(PARI) common(a, b)=a=vecsort(eval(Vec(Str(a))), , 8); b=vecsort(eval(Vec(Str(b))), , 8); #a+#b>#vecsort(concat(a, b), , 8)
in(v, x)=for(i=1, #v, if(v[i]==x, return(1))); 0
lista(nn) = {my(v=[37]); for(n=2, nn, forprime(p=2, default(primelimit), if(!in(v, p)&&common(v[#v], p), v=concat(v, p); break))); v; }
\\ Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A107353.

Other cases of seed: A107801 (a(1) = 2), A107802 (a(1) = 3), A107803 (a(1) = 5), A107804 (a(1) = 7), A107805 (a(1) = 11), A107806 (a(1) = 13), A107807 (a(1) = 17), A107808 (a(1) = 19), A107809 (a(1) = 23), A107810 (a(1) = 29), A107811 (a(1) = 31), A107813 (a(1) = 41), A107814 (a(1) = 43).

Sequence in context: A051316 A278067 A178199 * A254324 A356745 A068843

Adjacent sequences: A107809 A107810 A107811 * A107813 A107814 A107815

Keyword

nonn,base

Author

Zak Seidov and Eric Angelini, May 24 2005

Status

approved