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%I #11 Jan 20 2022 15:59:48
%S 3,17,31,59,997,2837,57349,83773,224813,861743,9999991,61879669,
%T 95895673,763137931,1463016067,1608398527,6909512173,38095693807,
%U 94041857089,4913845865567
%N Prime p such that the prime before p is a substring of p^3.
%C 10^18-11 and 10^31-27 are also terms. - _Giovanni Resta_, Nov 20 2018
%e Prime before 3 is 2 and it is a substring of 3^3 = 27.
%p P:=proc(q) local a,n; for n from 2 to q do a:=ithprime(n);
%p if searchtext(convert(prevprime(a),string),convert(a^3,string))>0
%p then print(a); fi; od; end: P(10^5);
%t sub[x_, y_] := StringPosition @@ ToString /@ {x, y} != {}; p = Prime@ Range@ 100000; p[[Select[Range[2, 100000], sub[p[[#]]^3, p[[# - 1]]] &]]] (* _Giovanni Resta_, Nov 20 2018 *)
%t Select[Prime[Range[700000]],SequenceCount[IntegerDigits[#^3],IntegerDigits[ NextPrime[ #,-1]]]>0&] (* The program generates the first 11 terms of the sequence; to generate all terms, increase the Range constant to 174344399360 but the program will take an extremely long time to run. *) (* _Harvey P. Dale_, Mar 27 2020 *)
%o (Python)
%o from itertools import count, islice
%o from sympy import prevprime, prime
%o def A321796_gen(): return filter(lambda p: str(prevprime(p)) in str(p**3), (prime(n) for n in count(2)))
%o A321796_list = list(islice(A321796_gen(),5)) # _Chai Wah Wu_, Jan 20 2022
%Y Cf. A052075.
%K nonn,base,more
%O 1,1
%A _Paolo P. Lava_, Nov 19 2018
%E a(10)-a(20) from _Giovanni Resta_, Nov 20 2018
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