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A320706
Indices of primes followed by a gap (distance to next larger prime) of 16.
2
282, 295, 319, 331, 335, 378, 409, 445, 476, 478, 481, 510, 560, 566, 619, 624, 674, 701, 739, 775, 856, 871, 881, 886, 935, 941, 1007, 1069, 1077, 1121, 1146, 1193, 1222, 1261, 1286, 1322, 1331, 1356, 1372, 1388, 1405, 1460, 1487, 1500, 1587, 1603, 1608, 1612, 1699, 1719, 1734, 1740, 1811, 1876, 1924, 1956, 1969, 1977, 2002, 2022, 2034, 2042, 2071
OFFSET
1,1
COMMENTS
Indices of the primes listed in A031934.
FORMULA
a(n) = A000720(A031934(n)).
A320706 = { i > 0 | prime(i+1) = prime(i) + 16 }.
MATHEMATICA
Select[Range[2500], Prime[#] + 16 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 19 2019 *)
Position[Partition[Prime[Range[2100]], 2, 1], _?(#[[2]]-#[[1]]== 16&), 1, Heads-> False]//Flatten (* Harvey P. Dale, Nov 01 2020 *)
PROG
(PARI) A(N=100, g=16, p=2, i=primepi(p)-1, L=List())={forprime(q=1+p, , i++; if(p+g==p=q, listput(L, i); N--||break)); Vec(L)} \\ returns the list of first N terms of the sequence
(Magma) [n: n in [1..2100] | NthPrime(n+1) - NthPrime(n) eq 16]; // Vincenzo Librandi, Mar 19 2019
CROSSREFS
Equals A000720 o A031934.
Row 8 of A174349.
Indices of 16's in A001223.
Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).
Sequence in context: A185710 A242982 A255387 * A356854 A114804 A250580
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 19 2018
STATUS
approved