A087556 a(n) = smallest prime that is the concatenation of two numbers whose sum is n.

11, 0, 13, 23, 0, 43, 17, 0, 19, 29, 0, 67, 59, 0, 79, 89, 0, 109, 137, 0, 139, 149, 0, 223, 179, 0, 127, 227, 0, 229, 131, 0, 277, 233, 0, 307, 137, 0, 139, 239, 0, 241, 359, 0, 379, 389, 0, 409, 149, 0, 151, 251, 0, 487, 353, 0, 157, 257, 0, 457, 359, 0, 163, 263, 0, 463

Offset

2,1

Comments

a(3k) = 0. Conjecture: No other term is zero.

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Example

a(10) = 19, the partitions of 10 are (1,9), (2,8), (3,7), (4,6), (5,5) and the primes obtained are 19, 37 and 73.

Mathematica

Table[Min[Select[#[[1]]*10^IntegerLength[#[[2]]]+#[[2]]&/@Flatten[{#, Reverse[#]}&/@IntegerPartitions[n, {2}], 1], PrimeQ]]/.\[Infinity]->0, {n, 2, 100}] (* Harvey P. Dale, Aug 02 2025 *)

Crossrefs

Cf. A087555.

Sequence in context: A271572 A180059 A147765 * A082268 A087557 A186072

Adjacent sequences: A087553 A087554 A087555 * A087557 A087558 A087559

Keyword

base,nonn

Author

Amarnath Murthy, Sep 13 2003

Extensions

More terms from David Wasserman, Jun 07 2005

Status

approved