A119890 Prime duet leaders: largest number of a prime duet.

11, 23, 41, 43, 61, 101, 113, 131, 151, 223, 241, 311, 313, 331, 401, 421, 601, 1013, 1031, 1033, 1051, 1103, 1123, 1213, 1231, 1301, 1303, 1321, 2003, 2111, 2113, 2131, 2203, 2221, 2311, 3011, 3121, 3301, 4001, 4003, 4021, 4111, 4201, 5011, 5101, 10103

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), May 27 2006

Keywords

• nonn
• base

Comments

A prime duet is a pair of two different prime numbers such that the second number is a 1-digit number which is the sum of the digits of the first number.

The terms of the sequence must be at least 2 digits in length, so {5,5} is not a prime duet. - Harvey P. Dale, May 07 2021

Examples

			113 is in the sequence because it is the largest number of the prime duet (113,5)
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 600 terms from Harvey P. Dale)
• L. Stevens, Prime ensembles
• David A. Corneth, PARI program

Crossrefs

Cf. A119889, A119891, A119892.

Programs

Mathematica

Select[Prime[Range[5,1300]],IntegerLength[Total[IntegerDigits[#]]]==1&&PrimeQ[Total[IntegerDigits[#]]]&] (* Harvey P. Dale, May 07 2021 *)

PARI

\\ See PARI link. David A. Corneth, May 07 2021

Extensions

Corrected by Harvey P. Dale, May 07 2021