A330293 a(1) = 1, a(2) = 2; for n > 2, a(n) = the smallest prime divisor of the number formed by the concatenation of a(1) to a(n-1) that has not previously appeared in the sequence.

1, 2, 3, 41, 7, 653, 331, 2536483, 191, 176081, 18307, 2143406938831, 101, 73, 3541, 439, 5665417, 37, 17302849, 86113, 11, 878390431, 2969, 1385625388248048145493629820571541645230648738185397486740279040908468652182116663161996667, 59, 30956837, 181, 151, 159833, 1629097816565791058167, 293, 2063, 3251, 31219483, 13

Offset: 1

Author

Scott R. Shannon, Dec 09 2019

Keywords

• nonn
• more
• hard
• base

Comments

The next term a(36) requires the factorization of a composite 246 digit number 18604...12467.

Examples

			a(3) = 3 as the concatenation of a(1) and a(2) = '12' and 3 is the smallest prime divisor of 12 that has not appeared in the sequence.
a(4) = 41 as the concatenation of a(1)..a(3) is '123' and 41 is the smallest prime divisor of 123 which has not appeared in the sequence. Note that 3 also divides 123 but a(3) = 3.
a(6) = 653 as the concatenation of a(1)..a(5) is '123417' and 653 is the smallest prime divisor of 123417 has not appeared in the sequence. Note that 9 also divides 123417 and has not appeared but only prime divisors are considered.
		

Crossrefs

Cf. A020639, A000040, A000005, A330290, A330291, A240588.