A108972 a(1) = 1; for n > 1, a(n) is the least k > a(n-1) such that a(n) + a(n-1) is square and a(n) - a(n-1) is prime.

1, 3, 6, 19, 30, 91, 134, 307, 318, 1051, 1158, 1867, 2358, 2971, 3590, 3979, 4670, 5131, 5478, 7747, 7878, 8251, 8390, 16891, 17334, 22267, 28358, 30691, 31310, 36811, 37718, 61507, 64518, 70171, 70454, 74707, 76614, 79411, 79790, 89131

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Example

Given a(5) = 30, the least k > 30 such that k + 30 is square and k - 30 is prime is 91 (91 + 30 = 121 = 11^2; and 91 - 30 = 61 is prime), so a(6) = 91.

Mathematica

a = 1; Print[a]; Do[k = a + 1; While[ !(PrimeQ[k - a] && IntegerQ[Sqrt[k + a]]), k++ ]; a = k; Print[a], {n, 1, 30}]

Crossrefs

Cf. A090956.

Sequence in context: A294570 A306968 A090956 * A304965 A203797 A019097

Adjacent sequences: A108969 A108970 A108971 * A108973 A108974 A108975

Keyword

nonn

Author

Ryan Propper, Aug 27 2005

Extensions

More terms from Robert G. Wilson v, Sep 28 2005

Status

approved