A289907 Initial primes of 5 consecutive primes with consecutive gaps 8,6,4,2.

1979, 5399, 11813, 41213, 42443, 44249, 47129, 55799, 57773, 74699, 79613, 84299, 88643, 126473, 143813, 148913, 167099, 176489, 178799, 178889, 209249, 211859, 237143, 266663, 267629, 272249, 272333, 322229, 344153, 348443, 354023, 375083, 391379, 399263, 422069, 449549, 521519, 529673

Offset

1,1

Comments

All terms = {23, 29} mod 30.

For initial primes of 5 consecutive primes with consecutive gaps 2,4,6,8 see A190814.

Number of terms less than 10^k: 0, 0, 0, 2, 13, 65, 317, 1563, 8671, 50643, ..., . - Robert G. Wilson v, Dec 07 2017

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 3114 terms from Muniru A Asiru)

Example

Prime(299..303) = { 1979, 1987, 1993, 1997, 1999 } and 1979 + 8 = 1987, 1987 + 6 = 1993, 1993 + 4 = 1997, 1997 + 2 = 1999.
Also, prime(5852..5856) = { 57773, 57781, 57787, 57791, 57793 } and 5773 + 8 = 57781, 57781 + 6 = 57787, 57787 + 4 = 57791, 57791 + 2 = 57793.

Mathematica

s = Prepend[Differences@ #, First@ #] & /@ Partition[Prime@ Range[10^5], 5, 1]; Select[s, Drop[#, 1] == Range[8, 2, -2] &][[All, 1]] (* Michael De Vlieger, Jul 14 2017 *)
p = {2, 3, 5, 7, 11}; lst = {}; While[ p[[1]] < 530000, If[ Differences@ p == {8, 6, 4, 2}, AppendTo[ lst, p[[1]] ]]; p = Join[Rest@ p, {NextPrime[ p[[-1]]] }]]; lst (* Robert G. Wilson v, Dec 07 2017 *)

Prog

(GAP)
I:=[8, 6, 4, 2];;
P:=Filtered([1..1000000], IsPrime);;
P1:=List([1..Length(P)-1], i->P[i+1]-P[i]);;  Collected(last);;
P2:=List([1..Length(P)-Length(I)], i->[P1[i], P1[i+1], P1[i+2], P1[i+3]]);;
P3:=List(Positions(P2, I), i->P[i]);
(PARI) is(n) = my(q); forstep(i=8, 2, -2, q=nextprime(n+1); if(q-n!=i, return(0)); n=q); return(1) \\ David A. Corneth, Jul 23 2017

Crossrefs

Cf. A078847, A153419, A190814, A190817, A190819, A190838.

Sequence in context: A343971 A343972 A225235 * A125490 A237334 A035870

Adjacent sequences: A289904 A289905 A289906 * A289908 A289909 A289910

Keyword

nonn

Author

Muniru A Asiru, Jul 14 2017

Status

approved