A280915 Primes where difference between largest digit and all other digits is a positive square.

11, 23, 37, 43, 59, 67, 73, 89, 101, 113, 127, 131, 149, 157, 167, 179, 197, 211, 239, 241, 257, 263, 269, 271, 293, 307, 311, 337, 347, 359, 373, 419, 421, 431, 449, 461, 491, 509, 523, 541, 571, 593, 607, 617, 641, 719, 733, 743, 751, 761, 809, 853, 941, 953, 971, 1013, 1021, 1031

Offset: 1

Author

Osama Abuajamieh, Jan 10 2017

Keywords

• nonn
• base

Comments

If the largest digit L (say) is repeated, the criterion is that that L - (sum of all digits except for one copy of L) is a square.

Examples

			Prime 1153 is in a(n) since 5-3-1-1=0. Zero is square.
Prime 1163 is in a(n) since 6-3-1-1=1. One is square.
Prime 1171 is in a(n) since 7-1-1-1=4. Four is square.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

This sequence is a parent sequence of A156753.

Programs

Mathematica

Select[Prime@ Range@ 175, IntegerQ@ Sqrt@ Fold[#1 - #2 &, Max@ #, Rest@ #] &@ Reverse@ Sort@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 02 2017 *)

PARI

is(n)=my(d=digits(n)); issquare(2*vecmax(d)-vecsum(d)) && isprime(n) \\ Charles R Greathouse IV, Feb 05 2017