A229947 -id:A229947

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A227869

Composite numbers congruent to 7 (mod 30).

+10
3

187, 217, 247, 427, 517, 637, 667, 697, 817, 847, 1027, 1057, 1147, 1177, 1207, 1267, 1357, 1387, 1417, 1477, 1507, 1537, 1687, 1717, 1807, 1837, 1897, 1927, 1957, 2047, 2077, 2107, 2167, 2197, 2227, 2257, 2317, 2407, 2497, 2527, 2587, 2737, 2827, 2947, 2977

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Up to 4897, there are more primes than composites among the numbers of the form 7+30k, only from 4927 on, composite numbers become more frequent.

See A132231 for primes of that form. See also A132237 (primes = 7 or 23 (mod 30)) and A229947 (primes not = 7 or 23 (mod 30)).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Table[30n + 7, {n, 100}], Not[PrimeQ[#]] &] (* Alonso del Arte, Nov 03 2013 *)

Select[Range[7, 3000, 30], CompositeQ] (* Harvey P. Dale, Oct 09 2023 *)

PROG

(PARI) forstep(p=7, 1999, 30, isprime(p)||print1(p", "))

KEYWORD

nonn

AUTHOR

M. F. Hasler, Nov 02 2013

STATUS

approved

A227868

Composite numbers congruent to 7 or 23 (mod 30).

+10
1

143, 187, 203, 217, 247, 323, 413, 427, 473, 517, 533, 623, 637, 667, 697, 713, 803, 817, 833, 847, 893, 923, 1027, 1043, 1057, 1073, 1133, 1147, 1177, 1207, 1253, 1267, 1313, 1343, 1357, 1387, 1403, 1417, 1463, 1477, 1507, 1537, 1643

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

It is remarkable that up to 4913, numbers congruent to 7 or 23 (mod 30) are more frequently prime than composite.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..2000

MATHEMATICA

Select[Range[2000], CompositeQ[#]&&MemberQ[{7, 23}, Mod[#, 30]]&] (* Harvey P. Dale, Sep 21 2024 *)

PROG

(PARI) for(p=1, 1999, setsearch([7, 23], p%30)&&!isprime(p)&&print1(p", "))

CROSSREFS

Cf. A132237, A229947.