A160432 -id:A160432 - cp's OEIS frontend

A309739 Primes of the form b10^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

3, 5, 7, 11, 13, 17, 19, 331, 661, 881, 991, 20201, 60601, 90901, 2002001, 5005001, 300030001, 600060001, 50000500001, 2000002000001, 8000008000001, 9000009000001, 3000000003000000001, 200000000020000000001, 80000000000800000000001

Offset: 1

Seiichi Manyama, Aug 15 2019

			b | Primes of the form b*10^(2*k) + b*10^k + 1
--+-------------------------------------------------------------
1 | 3.
2 | 5, 20201, 2002001, 2000002000001, 200000000020000000001, ...
3 | 7, 331, 300030001, 3000000003000000001.
4 |
5 | 11, 5005001, 50000500001, ...
6 | 13, 661, 60601, 600060001, ...
7 |
8 | 17, 881, 8000008000001, 80000000000800000000001, ...
9 | 19, 991, 90901, 9000009000001, 9000000000009000000000001, ...

Numbers k such that b*10^(2*k) + b*10^k + 1 are prime: A296444 (b=2), A309740 (b=5), A309741 (b=6), A309742 (b=8), A309743 (b=9).
Primes of the form b*10^(2*k) + b*10^k + 1: A160432 (b=3).
Cf. A309738.

A178509 Smallest value of k for which 6k+1 divides the subset of centered hexagonal terms included in A177019 that admit only factors like 6k+1.

Original entry on oeis.org

1, 55, 26, 5, 50005000, 1, 1, 16, 1936, 500000000500000000, 15333927, 1, 1, 18316, 3, 7, 1526, 1, 1, 12, 73, 38, 47, 1, 1, 121, 43502, 12, 11, 1, 1, 18, 3, 5, 10, 1, 1, 481, 2043419605725853, 921, 3835, 1, 1, 12, 10, 13, 25, 1, 1, 18, 3, 12, 62, 1, 1, 76, 398, 7

Offset: 0

Giacomo Fecondo, May 29 2010, May 30 2010

nonn

The terms a(0), a(1), a(4) and a(9) confirm the primality of the terms included in A160432;

k assumes the value 1 when the value of n in a(n) is equal to 6*i or 6*i-1 where i is a positive integer.

			a(0)= 1 so 6*1+1 = 7 is the minimum factor dividing 7; a(1)= 55 so 6*55+1 = 331 the minimum factor dividing 331; a(2)= 26 so 6*26+1 = 157 the minimum factor dividing 30301; a(3)= 5 so 6*5+1 = 31 the minimum factor dividing 3003001; a(10)=15333927 so 6*15333927+1 = 92003563 the minimum factor dividing 3*10^20+3*10^10+1.

Cf. A177019, A160432.

cp's OEIS Frontend

A309739 Primes of the form b10^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

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A178509 Smallest value of k for which 6k+1 divides the subset of centered hexagonal terms included in A177019 that admit only factors like 6k+1.

Views

Author

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Comments

Examples

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cp's OEIS Frontend

A309739 Primes of the form b*10^(2*k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

Views

Author

Keywords

Examples

Crossrefs

A178509 Smallest value of k for which 6*k+1 divides the subset of centered hexagonal terms included in A177019 that admit only factors like 6*k+1.

Views

Author

Keywords

Comments

Examples

Crossrefs

A309739 Primes of the form b10^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

A178509 Smallest value of k for which 6k+1 divides the subset of centered hexagonal terms included in A177019 that admit only factors like 6k+1.