A182320 Primes p = prime(n) such that the equation prime(n+k) - prime(n) = 6^(k-1) has at least one solution, k>0.

2, 5, 7, 11, 13, 17, 37, 41, 67, 97, 101, 103, 107, 191, 193, 223, 227, 277, 307, 311, 347, 457, 461, 613, 641, 773, 821, 823, 853, 857, 877, 881, 1013, 1087, 1091, 1277, 1297, 1301, 1373, 1423, 1427, 1447, 1481, 1483, 1487, 1607, 1663, 1693, 1811, 1867, 1871

Offset

1,1

Comments

The first term having k=5 as solution is larger than 10^9. - M. F. Hasler, May 20 2012

Links

Table of n, a(n) for n=1..51.

Example

a(1) = 2 = prime(1) = prime(1+1) - 6^(1-1) = 3 - 1 is the only term with k=1 as solution.
a(2) = 5 = prime(3) = prime(3+2) - 6^(2-1) = 11 - 6.
a(26) = 773 =  prime(137) =  prime(137+3) - 6^2 = 809 - 36 is the first term having k=3 as smallest solution.
10915517 = prime(721294) = prime(721294+4) - 6^3 = 10915733 - 216 is the first term having k=4 as solution. - M. F. Hasler, May 20 2012

Prog

(PARI) is_A182320(p)={isprime(p)||return; my(q=p); for(k=0, 9, p+6^k==(q=nextprime(q+1))&return(1))}  \\ M. F. Hasler, May 20 2012

Crossrefs

Cf. A001223, A182217.

Sequence in context: A197188 A265809 A303112 * A119993 A045346 A039675

Adjacent sequences: A182317 A182318 A182319 * A182321 A182322 A182323

Keyword

nonn

Author

Gerasimov Sergey, Apr 24 2012

Status

approved