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

Author

Muniru A Asiru, Jul 14 2017

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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]);

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 *)

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