OFFSET
1,1
COMMENTS
The second prime in this sequence, 144169, arises in the theory of modular forms, as observed by Hecke. On page 671 of Hecke (1937), Hecke works out the cusp forms of weight 24 and observes that the Hecke operators have eigenfunctions with Fourier coefficients in the quadratic field of discriminant 144169. Thanks to Jerrold B. Tunnell for this comment. See also the articles by Hida and Zagier. N. J. A. Sloane, Sep 13 2014
REFERENCES
E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung, Math. Annalen, 114 (1937), 1-28; Werke pp. 644-671. See page 671.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Haruzo Hida, Arithmetic of Weil numbers and Hecke fields.
Don Zagier, Elliptic Modular Forms and Their Applications
EXAMPLE
The first term is 6481 which is a prime and is the concatenation of 64 and 81 which are two consecutive square numbers.
MAPLE
catn:= proc(a, b) 10^(1+ilog10(b))*a+b end proc:
R:= NULL: count:= 0:
for x from 2 by 2 while count < 100 do
y:= catn(x^2, (x+1)^2);
if isprime(y) then count:= count+1; R:= R, y; fi
od:
R; # Robert Israel, May 19 2020
PROG
(Python)
from sympy import isprime
A104242_list = []
for n in range(1, 2000):
....x = int(str(n**2)+str((n+1)**2))
....if isprime(x):
........A104242_list.append(x) # Chai Wah Wu, Sep 13 2014
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Shyam Sunder Gupta, Apr 17 2005
STATUS
approved