A159922 Least index m such that the five numbers 2*prime(m+k) + 3^n, k=0 to 4, are five consecutive primes.

643266, 8813528, 1644953, 440421, 2826655, 1339785, 2775232, 988180, 196973, 643136, 4122122, 3477939, 182124, 6195602, 130854, 4937610, 2725523, 6118932, 231670, 478208, 2405748, 3913626, 1033788, 2945487, 22952758, 7168835, 15528738, 2753214, 2407038, 37795639

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Formula

a(1) = A102810(1) = A102811(5) = A089009(11). - R. J. Mathar, Apr 28 2009

Example

For n=15, prime(m=130854) = 1739401 starts the prime sequence 1739401, 1739411, 1739417, 1739443, 1739447 of five consecutive primes.
With 3^n = 3^15 = 14348907, the five numbers 17827709 = 2*1739401+14348907, 17827729 = 2*1739411 + 14348907, 17827741 = 2*1739417 + 14348907, 17827793 = 2*1739443 + 14348907, 17827801 = 2*1739447 + 14348907 are consecutive primes, and m = 130854 is the smallest prime index of this kind, so a(n=15) = 130854.

Prog

(PARI) a(n) = {my(m=1, p=[2, 3, 5, 7, 11], q, x=3^n); while(ispseudoprime(q=(2*p[1]+x)) + sum(k=2, 5, (q=nextprime(q+1))==2*p[k]+x) < 5, m++; p=concat(p[2..5], nextprime(p[5]+1))); m; } \\ Jinyuan Wang, Mar 20 2020

Crossrefs

Sequence in context: A089220 A052243 A102810 * A154873 A061406 A231323

Adjacent sequences: A159919 A159920 A159921 * A159923 A159924 A159925

Keyword

nonn

Author

Pierre CAMI, Apr 26 2009

Extensions

Edited by R. J. Mathar, Apr 28 2009

Replaced the wrong value 14348916 by 14348907 (3^15=14348907). - Pierre CAMI, May 09 2009

More terms from Jinyuan Wang, Mar 20 2020

Status

approved