A330291 -id:A330291 - cp's OEIS frontend

A330290 a(1) = 1; for n > 1, a(n) = the smallest divisor of the number formed by the concatenation of a(1) to a(n-1) that has not previously appeared in the sequence.

1, 1, 11, 101, 3, 9, 7, 61, 1821477701, 311, 449, 89, 29, 37, 121, 349, 1047, 73, 2741, 59, 5527, 21, 487, 3679724250117316595527, 137, 257, 33, 99, 27, 47, 17, 19, 13, 39, 63, 23, 557, 53, 159, 117, 351, 81, 3439913, 677, 83, 197, 151, 453, 211, 1033, 239296537198126662281, 167, 501

Offset: 1

Scott R. Shannon, Dec 09 2019

The next term a(54) requires the factorization of a composite 177 digit number 22177...67001.

			a(3) = 11 as the concatenation of a(1) and a(2) = '11' and 11, the smallest divisor of 11, has not appeared in the sequence.
a(4) = 101 as the concatenation of a(1)..a(3) is '1111' and 101 is the smallest divisor of 1111 which has not appeared in the sequence. Note that 11 also divides 1111 but a(3) = 11.
a(6) = 9 as the concatenation of a(1)..a(5) is '11111013' and 9 is the smallest divisor of 11111013 which has not appeared in the sequence. Note that 3 also divides 11111013 but a(5) = 3.

Cf. A020639, A000040, A000005, A330291, A330293, A240588.

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.

Original entry on oeis.org

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

Scott R. Shannon, Dec 09 2019

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

			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.

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

cp's OEIS Frontend

A330290 a(1) = 1; for n > 1, a(n) = the smallest divisor of the number formed by the concatenation of a(1) to a(n-1) that has not previously appeared in the sequence.

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