A022011 -id:A022011 - cp's OEIS frontend

A357890 a(n) = (A022013(n) - 173)/210.

422, 1355, 4074, 5460, 31242, 329316, 353648, 1038255, 1246060, 1440679, 4593664, 6382389, 6669205, 6773694, 8748381, 9343041, 10085055, 10711252, 10819136, 12181959, 12804411, 13683806, 14044105, 15616253, 19232028, 20795482, 21014272, 25076295, 26366476, 27457318

Offset: 1

Hugo Pfoertner, Nov 18 2022

nonn

Linear conversion of the initial members of prime octuplets of type p + {0, 6, 8, 14, 18, 20, 24, 26}.

Numbers k such that 210*k+173, 210*k+179, 210*k+181, 210*k+187, 210*k+191, 210*k+193, 210*k+197, and 210*k+199 are all primes. - Jianing Song, Nov 18 2022

Norman Luhn, Patterns of prime k-tuplets & the Hardy-Littlewood constants.

Cf. A022011, A022012, A022013.
Cf. A182393 (similar for type p + {0, 2, 6, 8, 12, 18, 20, 26}).
Cf. A145315 (minus 1, similar for type p + {0, 2, 6, 12, 14, 20, 24, 26}).
Subsequence of A357889.

A375344 First term p1 of octuplets of consecutive prime numbers pi with given successive gaps pi-p1, i=2, ...,8 (6, 8, 18, 24, 30, 36, 38).

Original entry on oeis.org

233, 2721413, 154670903, 200559053, 232777673, 273788363, 299267663, 459117353, 527326403, 1015923113, 1563572243, 1688692763, 2426018723, 2918492243, 3743134523, 4445599853, 4458163943, 4697619593, 5493835013, 5546977823, 5930389313, 6131660663, 6470661143, 7598587943

Offset: 1

René-Louis Clerc, Aug 12 2024

nonn

The choice of successive gaps (6, 8, 18, 24, 30, 36, 38) is such that the sum of the eight prime numbers beginning with 233 is 2024. The next year being the sum of analogous octuplet is 21771464 (21772nd millenium).

			233, 239, 241, 251, 257, 263, 269, 271 (sum = 2024).
2721413, 2721419, 2721421, 2721431, 2721437, 2721443, 2721449, 2721451 (sum = 21771464).

René-Louis Clerc and Jean-Baptiste Hiriart-Urruty, The octuplet of the year 2024 and its relatives, pp. 1-10, hal-04666530, 2024.

Cf. A000040, A001223, A002476, A151800, A000720, A065706, A022011.

uplet(p)= {n=0;for(i=p, p+38, if(isprime(i), n+=1));n}
octo(m)={for(p=3,p=10^m,if(isprime(p) && isprime(p+6) && isprime(p+8) && isprime(p+18) && isprime(p+24) && isprime(p+30) && isprime(p+36) && isprime(p+38) && uplet(p)==8,print1(p,", ")))}
listocto(p1)=print1(p1,", ", p1+6,", ", p1+8,", ", p1+18,", ", p1+24,", ", p1+30,", ", p1+36", ", p1+38)

cp's OEIS Frontend

A357890 a(n) = (A022013(n) - 173)/210.

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