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

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

Offset

1,1

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)

Links

Table of n, a(n) for n=1..9.

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A126127 A230324 A060256 * A093324 A169676 A355912

Adjacent sequences: A103896 A103897 A103898 * A103900 A103901 A103902

Keyword

nonn,base,more

Author

Zak Seidov, Mar 30 2005

Extensions

4 more terms from Ryan Propper, Aug 10 2005

Status

approved