A103899 Concatenation of next a(n) odd numbers is prime.

2, 1, 1, 2, 1, 50, 2, 13, 10

Offset: 1

Author

Zak Seidov, Mar 30 2005

Keywords

• nonn
• base
• more

Comments

From Vladimir Shevelev and Peter J. C. Moses, Sep 30 2014: (Start)

Consider a partition of consecutive odd numbers in minimal blocks such that concatenation of numbers in each block is a prime. The sequence lists the numbers of odd numbers in each block.

The first blocks are |1,3|5|7|9,11|13|15,17,...,111,113|115,117|, etc.

The prime corresponding to a(6) has 107 digits; a(10) has more than 58759 digits.

(End)

Examples

			a(1)=2 because 13 is prime.
Then we have p(2)=5, p(3)=7, p(4)=911, p(5)=13. The primes obtained for n=7 to 9 are: 115117, 119121123125127129131133135137139141143, 145147149151153155157159161163. The next prime to find should begin with "165". Next term a(10), if it exists, is > 1000. - _Michel Marcus_, Oct 05 2013
		

Programs

Mathematica

c = 1; Do[p = c; k = 1; While[ !PrimeQ[p], c += 2; p = p*10^Length[IntegerDigits[c]] + c; k++ ]; Print[k]; c += 2, {n, 1, 30}] (* Ryan Propper, Aug 10 2005 *)

PARI

findn(n) = {new = n; conc = n; while (! isprime(conc), new += 2; conc = eval(concat(Str(conc), Str(new)));); print1(conc, ", "); new+2;}
lista(nn) = {odd = 1; for (i = 1, nn, nodd = findn(odd); nb = (nodd - odd)/2; print1(nb, ", "); odd = nodd; print("new odd ", odd););} \\ Michel Marcus, Oct 05 2013

Extensions

4 more terms from Ryan Propper, Aug 10 2005