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A052073 Primes p with the property that nextprime(p) is a substring of p^2. 5
23, 83, 113, 1123, 200003, 328127, 381289, 714597769, 4916552822383 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(10) > 4*10^13. The prime 482564152712479922509389813571 is also a term. - Giovanni Resta, May 24 2018

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

381289 is a term because nextprime(381289) = 381301 is a substring of 381289^2 = 145381301521.

MAPLE

P:=proc(q) local a, b, k, n; a:=2; b:=3;

for n from 1 to q do for k from 1 to ilog10(a^2)-ilog10(b)+1 do

if b=trunc(a^2/10^(k-1)) mod 10^(ilog10(b)+1) then print(a); fi; od;

a:=b; b:=nextprime(b); od; print(); end: P(10^9);

# Paolo P. Lava, May 24 2018

MATHEMATICA

Select[Prime@Range[1000000],

StringContainsQ[ToString[#^2], ToString[NextPrime[#]]] &] (* Robert Price, Oct 12 2019 *)

CROSSREFS

Cf. A052074, A052075, A052076.

Sequence in context: A304592 A302729 A139940 * A213174 A256376 A128825

Adjacent sequences:  A052070 A052071 A052072 * A052074 A052075 A052076

KEYWORD

nonn,base,more,changed

AUTHOR

Patrick De Geest, Jan 15 2000

EXTENSIONS

a(8) from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 04 2006

a(9) from Giovanni Resta, May 24 2018

STATUS

approved

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Last modified October 17 21:16 EDT 2019. Contains 328132 sequences. (Running on oeis4.)