A089721 Primes ending in 1 such that floor(p/7) ends in a digit > 3.

31, 41, 61, 101, 131, 181, 191, 241, 251, 271, 311, 331, 401, 461, 521, 541, 601, 661, 691, 751, 761, 811, 821, 881, 941, 971, 1021, 1031, 1091, 1151, 1171, 1181, 1231, 1291, 1301, 1321, 1361, 1381, 1451, 1511, 1531, 1571, 1601, 1721, 1741, 1801, 1811

Offset

1,1

Comments

Original definition: Pseudofactor sets of primes ending in 1: 7 greater than 3.

These pseudofactors, although not unique sets as their domains seem to overlap, form twelve subsets of primes based on the first digit set {1,3,7,9} when {2,5} are taken away from the prime set. This is one of the four {1}'s sets. There exist {3}'s, {7}'s and {9}'s sets of these same four types.

Primes ending in 1 are listed if Mod[floor(a[n]/7), 10]>3, where Mod is the binary "remainder" operator.

Primes == 31, 41, 51 or 61 (mod 70). - Robert Israel, Jun 14 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

select(isprime, [seq(seq(70*i+j, j=[31, 41, 51, 61]), i=0..100)]); # Robert Israel, Jun 14 2019

Mathematica

digits=4*200 a=Delete[Union[Table[If[Mod[Prime[n], 10]==1, Prime[n], 0], {n, 1, digits}]], 1] d2=Dimensions[a][[1]] a7g3=Delete[Union[Table[If[Mod[a[[n]]/7, 10]>3, a[[n]], 0], {n, 1, d2}]], 1]
pe1Q[n_]:=Mod[n, 10]==1&&Mod[Floor[n/7], 10]>3; Select[Prime[Range[ 300]], pe1Q] (* Harvey P. Dale, Mar 26 2012 *)

Prog

(PARI) forprime( p=1, 9999, p%10==1 & p\7%10>3 & print1(p", ")) \\ M. F. Hasler, Apr 06 2009

Crossrefs

Sequence in context: A340444 A109550 A040991 * A089442 A243704 A060327

Adjacent sequences: A089718 A089719 A089720 * A089722 A089723 A089724

Keyword

nonn,base

Author

Roger L. Bagula, Jan 06 2004

Extensions

Corrected and edited by M. F. Hasler, Apr 06 2009

Status

approved