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A289907 Initial primes of 5 consecutive primes with consecutive gaps 8,6,4,2. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 11 03:41 EDT 2022. Contains 356046 sequences. (Running on oeis4.)