A104227 -id:A104227 - cp's OEIS frontend

A104229 Primes equal to the product of two successive sexy primes plus 6.

61, 97, 193, 397, 673, 1153, 1597, 1933, 4093, 7393, 12097, 37633, 64513, 70753, 96097, 122497, 126733, 136897, 190093, 211597, 256033, 313597, 329473, 348097, 430333, 541693, 781453, 891133, 988033, 1267873, 1416097, 1674433, 2102497

Offset: 1

Giovanni Teofilatto, Apr 02 2005

Primes of the form 6 + A111192(i). - R. J. Mathar, Nov 26 2008

All numbers in this sequence are of the form 12n + 1. Also, as one would expect from a random distribution of sexy prime pairs, with the exception of 61, in decimal two thirds of these numbers end in 3, and the other third end in 7. - Daniel Mondot, Apr 29 2024

Daniel Mondot, Table of n, a(n) for n = 1..10000

Cf. A023201, A046117, A104227, A104228, A111192.

Extended by R. J. Mathar, Nov 26 2008

A104228 Primes one larger than the sum over a sexy prime pair.

Original entry on oeis.org

17, 29, 41, 53, 89, 101, 113, 173, 269, 353, 389, 461, 509, 521, 701, 773, 929, 1013, 1181, 1193, 1289, 1301, 1361, 1721, 1889, 1901, 1949, 2213, 2381, 2441, 2609, 2729, 2741, 2861, 2969, 3209, 3221, 3821, 4001, 4133, 4421, 4481, 4673, 4793, 4889, 5381, 5393, 5801, 5813, 6173, 6653, 7349, 7529

Offset: 1

Giovanni Teofilatto, Apr 02 2005

Primes of the form A023201(i)+A046117(i)+1 - R. J. Mathar, Nov 26 2008

			17=5+11+1 is prime and one larger than the sum 5+11 over the first sexy prime pair. - _R. J. Mathar_, Nov 26 2008

Cf. A023201, A046117, A104227, A104229.

Inserted 89 and extended beyond a(8). - R. J. Mathar, Nov 26 2008

A104047 Primes p equal to the sum of two successive sexy primes - 1 such that p - 6 is also prime.

Original entry on oeis.org

19, 67, 79, 199, 547, 619, 739, 1459, 1759, 3319, 3739, 4027, 4567, 5107, 5419, 6367, 7219, 8719, 9187, 9907, 10459, 10867, 11119, 12547, 13099, 14827, 15739, 16927, 17047, 18307, 21319, 25939, 27259, 27367, 31327, 33967, 37579, 38839, 38959

Offset: 1

Giovanni Teofilatto, Mar 31 2005

Cf. A023201, A046117.

Select[2#+5&/@Select[Prime[Range[4200]],PrimeQ[#+6]&],And@@PrimeQ[ {#,#-6}]&] (* Harvey P. Dale, Feb 28 2012 *)

A104227 INTERSECT A046117. [From R. J. Mathar, Nov 26 2008]

23 and 29 removed, extended by R. J. Mathar, Nov 26 2008

A375091 First element p of sexy prime pairs (p,p+6) whose concatenation is also prime.

Original entry on oeis.org

11, 13, 17, 31, 83, 97, 101, 151, 157, 167, 223, 227, 233, 251, 257, 263, 271, 331, 353, 373, 433, 461, 541, 601, 653, 677, 727, 821, 823, 877, 941, 971, 1013, 1033, 1181, 1187, 1223, 1367, 1447, 1453, 1657, 1693, 1741, 1861, 1973, 1993, 1997, 2207, 2281, 2333, 2393, 2441

Offset: 1

James S. DeArmon, Jul 29 2024

			11 is the first term, since (11,17) are sexy primes and 1117 is also prime.
The second term is 13, since 1319 is prime.

Intersection of A023201 and A032621.

Cf. A031924, A104227, A032629.

q:= p-> andmap(isprime, [p, p+6, parse(cat(p, p+6))]):
select(q, [$2..3000])[];  # Alois P. Heinz, Aug 02 2024

Select[Prime[Range[370]], PrimeQ[#+6] && PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[#+6]]]] &] (* Stefano Spezia, Aug 03 2024 *)

isp(p) = isprime(p+6) && isprime(eval(concat(Str(p), Str(p+6))))
select(isp, primes(100)) \\ Michel Marcus, Aug 02 2024

from sympy import isprime
def ok(n): return isprime(n) and isprime(n+6) and isprime(int(str(n)+str(n+6)))
print([k for k in range(2500) if ok(k)]) # Michael S. Branicky, Aug 01 2024

cp's OEIS Frontend

A104229 Primes equal to the product of two successive sexy primes plus 6.

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A104228 Primes one larger than the sum over a sexy prime pair.

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A104047 Primes p equal to the sum of two successive sexy primes - 1 such that p - 6 is also prime.

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A375091 First element p of sexy prime pairs (p,p+6) whose concatenation is also prime.

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