A241007 Decimal encoding of the prime factorization of a(n) is a prime.

3, 6, 7, 8, 13, 19, 20, 31, 35, 38, 40, 43, 44, 45, 56, 60, 63, 65, 68, 69, 96, 97, 103, 104, 109, 116, 119, 122, 125, 133, 138, 151, 157, 159, 160, 171, 174, 181, 189, 193, 204, 209, 211, 212, 215, 216, 220, 221, 232, 241, 248, 250, 254, 267, 271, 273, 280

Offset: 1

Author

Paolo P. Lava, Aug 07 2014

Keywords

• nonn
• easy
• base

Comments

This sequence gives all arguments for which A067599 is prime: A067599(a(n)) = prime. - Wolfdieter Lang, Aug 16 2014

Examples

			Prime factorization of a(4) = 8 is 2^3 and its decimal encoding is A067599(8) = 23 that is prime.
Prime factorization of a(188) = 994 is 2^1*7^1*71^1 and its decimal encoding is  A067599(994) = 2171711 that is prime.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067598, A067599.

Programs

Maple

with(numtheory); P:=proc(q) local a,b,c,d,k,j,n;
for n from 1 to q do a:=(ifactors(n)[2]); b:=[];
for k from 1 to nops(a) do b:=[op(b),a[k,1]]; od; b:=sort(b); c:=0;
for k from 1 to nops(b) do d:=1; while b[k]<>a[d,1] do d:=d+1; od;
j:=b[k]*10^(ilog10(a[d,2])+1)+a[d,2];
c:=c*10^(ilog10(j)+1)+j; od; if isprime(c) then print(n);
fi; od; end: P(1000);

Formula

Sequence of the members of the set {k >= 2: A067599(k) is a prime} in increasing order. - Wolfdieter Lang, Aug 16 2014

Extensions

Edited: Name n-> a(n), cf. A067599, examples specified. - Wolfdieter Lang, Aug 16 2014