A108022 a(1)=2; a(n) is the smallest prime such that a(n)-a(n-1) is a 4th power (>0).

2, 3, 19, 160019, 1049920019, 1050730019, 1051540019, 12910750019, 13960510019, 14167870019, 67252030019, 67252840019, 67318450019, 196918450019, 197968210019, 568118770019, 568119580019, 938270140019, 938477500019

Offset

1,1

Comments

All members after 19 will end in '0019'.

Also, for n > 3, a(n) - a(n - 1) = k^4, k is a multiple of 30. - Zak Seidov, Apr 09 2013

Links

Table of n, a(n) for n=1..19.

Example

a(3)=19, for 19 +k^4 to be prime, k must be even and divisible by 5. 19+10^4=10019=43*233,but 19+20^4 is prime.

Mathematica

Join[{2, 3, 19, p=160019}, Table[x=30; While[!PrimeQ[q=p+x^4], x=x+30]; p=q, {19}]] (* Zak Seidov, Apr 09 2013 *)

Crossrefs

Cf. A073609, A076201.

Sequence in context: A254380 A099069 A038584 * A108884 A119584 A344546

Adjacent sequences: A108019 A108020 A108021 * A108023 A108024 A108025

Keyword

nonn

Author

John L. Drost, May 31 2005

Status

approved