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A179632

Primes p such that p + the integer part of square root of its digits is a prime.

2, 5, 11, 19, 67, 101, 109, 127, 163, 457, 557, 587, 593, 599, 613, 647, 677, 823, 857, 877, 941, 971, 1009, 1097, 1187, 1213, 1277, 1291, 1367, 1427, 1453, 1481, 1483, 1543, 1553, 1559, 1663, 1741, 1753, 1783, 1861, 1871, 1873, 1907, 2083, 2267, 2287, 2377, 2393, 2417, 2441, 2459

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..10000

EXAMPLE

67 is in the sequence since 67 + floor(sqrt(6)) + floor(sqrt(7)) = 67+2+2 = 71 is prime.

MATHEMATICA

Select[Prime[Range[500]], PrimeQ[# + Total[Floor[Sqrt[IntegerDigits[#]]]]] &] (* Paolo Xausa, Jan 13 2026 *)

PROG

(PARI) isok(n) = {if (isprime(n), digs = digits(n, 10); isprime(n + sum(i=1, #digs, sqrtint(digs[i]))); , 0; ); } \\ Michel Marcus, Jul 18 2013

CROSSREFS