A060235 Smallest primes whose residue modulo its difference from the next prime is 2n-1.

3, 7, 23, 199, 139, 467, 293, 1951, 1259, 2179, 3739, 3271, 12011, 45779, 18869, 14107, 62233, 27143, 34981, 44293, 102701, 25471, 91033, 117443, 107377, 445363, 181303, 153001, 399793, 195599, 273367, 531383, 537413, 633667, 302329, 576791

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Formula

Min_{p | p mod (nextprime(p) - p) = 2n-1};

a(n) is the least prime with A000040(n) mod A001223(n) = 2n-1.

Example

The residue p mod d = 5 = 2*3 - 1 for primes {23, 57, 53, 83, ...} of which the first one is 23, so a(3)=23.

Mathematica

Module[{nn=100000, pm}, pm={#[[1]], Mod[#[[1]], #[[2]]-#[[1]]]}&/@Partition[ Prime[Range[nn]], 2, 1]; Table[SelectFirst[pm, #[[2]]==2n-1&], {n, 40}]] [[All, 1]] (* Harvey P. Dale, Aug 07 2019 *)

Prog

(PARI) a(n) = {my(p = 2); forprime(q=3, , if (q % (q-p) == (2*n-1), return (p)); p = q; ); } \\ Michel Marcus, Jul 09 2018

Crossrefs

Cf. A000040, A001223.

Sequence in context: A113824 A121883 A262264 * A343815 A090188 A001773

Adjacent sequences: A060232 A060233 A060234 * A060236 A060237 A060238

Keyword

nonn

Author

Labos Elemer, Mar 21 2001

Extensions

Offset 1 by Michel Marcus, Jul 09 2018

Status

approved