A261192 a(0) = 2; for n>0, a(n) = smallest prime p such that p > a(n-1) and p is congruent to n modulo prime(n).

2, 3, 5, 13, 53, 71, 97, 109, 179, 193, 271, 383, 419, 587, 659, 673, 811, 1433, 1543, 1627, 2221, 2357, 4051, 4339, 4919, 5651, 5783, 6619, 6983, 7877, 8053, 11969, 12739, 12911, 14629, 15233, 15287, 15737, 18131, 18743, 20627, 21163, 21943, 22963, 23011, 23291, 25717, 26633, 27031, 27743

Offset: 0

Author

Ivan N. Ianakiev and Robert G. Wilson v, Aug 11 2015

Keywords

• nonn

Comments

a(n) == A186102(n) == A260416(n) (mod n).

a(10314) = 10000363333.

Examples

			a(4) = 53 because prime(4) = 7, 53 == 4 (mod 7) and 53 is the smallest such prime greater than a(3) = 13.
		

Links

• Ivan N. Ianakiev and Robert G. Wilson v, Table of n, a(n) for n = 0..100000

Crossrefs

Cf. A186102, A260416.

Programs

Mathematica

f[n_] := f[n] = Block[{k = Prime@ n, q = Prime@ n}, While[k + n <= f[n - 1] || ! PrimeQ[k + n], k += q]; k + n]; f[0] = 2; Array[f, 50, 0]