A158473 Primes whose digit sum contains one or more digits of the same prime.
2, 3, 5, 7, 19, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 271, 281, 283, 307, 317, 337, 347, 367, 373, 379, 397, 419, 461, 463, 467, 491, 541, 557, 571, 613, 617, 619, 631, 641, 643, 647, 661, 673, 691, 719, 733, 739, 743, 751
Offset: 1
Examples
139 is a prime whose digit sum of 13 contains the digits 1 and 3 which are also in the prime. 149 is a prime whose digit sum of 14 contains the digits 1 and 4 which are also in the prime. 419 is a prime whose digit sum of 14 contains the digits 1 and 4 which are also in the prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- Chris Caldwell, The First 1,000 Primes
Programs
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Maple
filter:= proc(n) local L,s; L:= convert(n,base,10); s:= convert(L,`+`); convert(convert(s,base,10),set) intersect convert(L,set) <> {} end proc: select(filter, [seq(ithprime(i),i=1..100)]); # Robert Israel, Feb 27 2023 -
PARI
isok(p) = isprime(p) && (#setintersect(Set(digits(p)), Set(digits(sumdigits(p)))) >= 1); \\ Michel Marcus, Nov 12 2017
Extensions
Single-digit primes added by R. J. Mathar, Jul 08 2009
Typos in data corrected by D. S. McNeil and Andrew Weimholt, Aug 17 2010