A173919 Numbers that are prime or one less than a prime.

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 19, 22, 23, 28, 29, 30, 31, 36, 37, 40, 41, 42, 43, 46, 47, 52, 53, 58, 59, 60, 61, 66, 67, 70, 71, 72, 73, 78, 79, 82, 83, 88, 89, 96, 97, 100, 101, 102, 103, 106, 107, 108, 109, 112, 113, 126, 127, 130, 131, 136, 137, 138, 139

Offset: 1

Author

Giovanni Teofilatto, Mar 02 2010

Keywords

• nonn
• easy

Comments

Indices of the triangular numbers in A147846.

Integers k such that k or k+1 is prime. - Giovanni Teofilatto, Mar 05 2010

For a given common difference d, there always exists a longest possible arithmetic progression (AP) of primes, and the number of elements k in this AP of primes is necessarily a term of this sequence. See A123556 for explanations. - Bernard Schott, Mar 18 2023

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000.
• Diophante, A1880. NP (Nombres Premiers) en PA (Progression Arithmétique) (in French).
• Wikipedia, Primes in arithmetic progression.
• Index entries for sequences related to primes in arithmetic progressions.

Crossrefs

Cf. A000217, A147846.

Cf. A040976, A123556, A360735.

Complement to A068780. [Giovanni Teofilatto, Mar 11 2010]

Programs

Mathematica

{#-1,#}&/@Prime[Range[40]]//Flatten//Union (* Harvey P. Dale, Dec 21 2018 *)

Formula

A006093 U A000040.

Extensions

Definition corrected and sequence extended by R. J. Mathar, Feb 24 2010, Mar 05 2010