A277111 Lesser of twin primes P(k) and P(k+1) such that Sd(P(k)) + Sd(P(k+1)) = Sd(k) + Sd(k+1), where Sd(x) is the sum of digits of x.

1619, 2309, 2339, 12239, 28109, 35081, 37307, 37571, 50549, 51059, 51719, 62129, 64919, 65729, 87539, 89519, 91079, 113759, 121439, 121631, 160649, 170351, 174329, 182129, 191249, 205949, 215459, 223679, 231839, 254039, 270269, 285119, 301841, 317489, 319829

Offset: 1

Author

Paolo P. Lava, Sep 30 2016

Keywords

• nonn
• base
• easy

Examples

			P(256) = 1619, P(257) = 1621; Sd(256) + Sd(257) = 13 + 14 = 27 and Sd(1619) + Sd(1621) = 17 + 10 = 27.
		

Links

• Paolo P. Lava, First 60 couples [k, P(k)]

Crossrefs

Cf. A001359, A033548.

Programs

Maple

T:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=y+(x mod 10); x:=trunc(x/10); od; y; end:
P:= proc(q) local a,b,k,n;
for n from 1 to q do if ithprime(n+1)-ithprime(n)=2 then if T(ithprime(n))+T(ithprime(n+1))=T(n)+T(n+1) then print(ithprime(n)); fi; fi; od; end: P(10^5);